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Full text of "Earthquake engineering of large underground structures"

Report No. FHWA/RD-80/195 

EARTHQUAKE ENGINEERING OF 
LARGE UNDERGROUND STRUCTURES 



January 1981 
Final Report 



Earth's Surface 
Underground Site 




DEPARTMENT OF 
TRANSPORTATION 

Dte 1 tod i 

LIBRARY 



Document is available to the public through 
the National Technical Information Service, 
Springfield, Virginia 22161 




Prepared for 

FEDERAL HIGHWAY ADMINISTRATION 
Offices of Research & Development 
Structures and Applied Mechanics Division 
Washington, D.C. 20590 

NATIONAL SCIENCE FOUNDATION 
1800 G Street, N.W. 
Washington, D.C. 20550 



FOREWORD 



This report is the result of research conducted by URS/John A. Blume 
Associates, Engineers, for the Federal Highway Administration (FHWA), 
Office of Research, under FHWA agreement 7-1-05-14 and the National 
Science Foundation (NSF) under NSF PFR-7706505. The report will 
be of interest to those researchers and engineers concerned with 
assessing the vulnerability of underground tunnels to strong ground 
motion. Specifically, the current state-of-the-art of earthquake 
engineering of transportation tunnels and other large underground 
structures is evaluated. 

Copies of the report are being distributed by FHWA transmittal 

memorandum.' Additional., copies may be obtained from the National 

Technical Information Service, 5285 Port Royal Road, Springfield, 
Virginia 22161. 



Charles F. ScheJ 

Director, Office of Research 

Federal Highway Administration 




NOTICE 

This document is disseminated under the sponsorship of the Department 
of Transportation in the interest of information exchange. The 
United States Government assumes no liability for its contents or 
use thereof. The contents of this report reflect the views of the 
contractor, who is responsible for the accuracy of the data pre- 
sented herein. The contents do not necessarily reflect the official 
views or policy of the Department of Transportation. This report 
does not constitute a standard, specification, or regulation. 

The United States Government does not endorse products or manufacturers 
Trade or manufacturers' names appear herein only because they are 
considered essential to the object of this document. 



43 



Technical Report Documentation Page 



1. Report No. 



FHWA/RD-80/195 



2. Government Accession No. 



3. Recipient's Catalog No. 



4. Title and Subtitle 



5. Report Date 



Earthquake Engineering of Large Underground 
Structures 



January 1981 



6. Performing Orgoni zotion Code 



7. Author's) 



G. Norman Owen and Roger E. Schol 1 



8. Performing Organization Report No. 

JAB-7821 



9. Performing Organization Name and Address 

URS/John A. Blume & Associates, Engineers 

130 Jessie Street 

San Francisco, California 9^105 



10. Work Unit No. (TRAIS) 

3563-^12 



1 1 . Controct 



12. Sponsoring Agency Name ond Address Federal HiohwaV 

National Science Administration 

Foundation and Department of 

Transportat ion 



Washington, D.C. 20550 



Washington, D.C. 2059< 




Period Covered 

September 1980 
Report 



0H38 



15. Supplementary Notes 



National Science Foundation Program Manager: Dr. William W. Hakala (202) 357 - 7737 
Federal Highway Administration Contract Manager: Mr. James D. Cooper (703) 557~5272 



16. Abstract 

This study identifies and evaluates the current state of the art of earthquake 
engineering of transportation tunnels and other large underground structures. A 
review of the past performance of 127 underground openings during earthquakes indi- 
cates that underground structures in general are less severely affected than surface 
structures at the same geographic location. However, some severe damage, including 
collapse, has been reported. Stability of tunnels during seismic motion is affected 
by peak ground motion parameters, earthquake duration, type of support, ground con- 
ditions, and in situ stresses. 

The literature on the nature of underground seismic motion is reviewed in detail. 
Although recorded underground motions tend to substantiate the idea that motion does 
reduce with depth, amplification at depth has been observed. 

The current procedures used in the seismic design of underground structures vary 
greatly depending upon the type of structure and the ground conditions. Procedures 
for subaqueous tunnels are fairly well formulated; however, procedures for structures 
in soil and rock are not as well formulated. Numerical procedures to predict dynamic 
stresses are not completely compatible with current static design procedures, which 
are more strongly affected by empirical methods than by stress-prediction models. 

Recommended research activities include the systematic reconnaissance of under- 
ground structures following major earthquakes, the placement of instrumentation for 
recording seismic motion in tunnels, analytical studies of underground motion, and 
the further development of seismic design procedures for structures in soil and rock. 



17. Key Words 

Earthquake Engineering, Underground 
Structures, Earthquake Effects, 
Seismic Response, Submerged 
Tunnels, Tunnels in Soil, Tunnels in 
Rock, Seismic Design 



19. Security Clossif. (of this report) 

Unclassified 



18. Distribution Statement 

Document is available to public 

through the National Technical 

Information Service, Springfield, 
VA 22161 



20. Security Clossif. (of this poge) 

Unclassified 



21. No. of Pages 

287 



22. Pr 



Porm DOT F 1700.7 (8-72) 



Reproduction of completed page authorized 



Contents 

page 
ACKNOWLEDGEMENTS i x 

SUMMARY , . , , , , . xi 

Effects of Earthquakes on Underground Structures xi 

Variation of Seismic Motion with Depth xii 

Seismic Wave Study of a Circular Cavity xiii 

Analytical and Design Procedures for Underground Structures xiv 

Critique of the State of the Art xv 

Research Recommendations xvi 

1. INTRODUCTION 1 

2. BACKGROUND INFORMATION . 3 

Underground Structures 3 

Seismic Activity and Earthquake Hazard 5 

Earthquake Magnitude and Intensity 11 

3. OBSERVED EFFECTS OF EARTHQUAKES AND UNDERGROUND EXPLOSIONS 13 

Effects of Earthquakes 13 

Response Parameters 1 k 

Summary of Available Data ; 16 

Effects of Underground Explosions 22 

Conventional Blasting 23 

High-Explosive Tests , 23 

Underground Nuclear Explosions 27 

Summary and Conclusions 35 

k. SEISMIC ANALYSIS 38 

Current Techniques Used in Seismic Analysis 38 

Available Numerical Models 38 

Analysis of Free-Field Stresses and Strains 39 

Seismic Analysis of Underground Structures kS 

Properties Required for Seismic Analysis 64 

Techniques for Measuring Soil and Rock Properties 64 

Problems in Synthesizing Measured Properties 70 



- i i - 



CONTENTS (Continued) 

page 

5. SEISMIC WAVE PROPAGATION 7k 

The Nature of Underground Motion ~]k 

Factors Affecting Underground Motion ~lk 

Prediction of Underground Motion 80 

Depth-Dependence of Underground Motion 82 

Literature Review 82 

Theoretical Formulation of Depth Dependence 86 

Parametric Studies of Depth Dependence 92 

Dynamic Response of Underground Cavities 105 

Literature Review 107 

Theoretical Formulation of Cavity Response . ., 1 08 

Numerical Study of Cavity Response 113 

6. CURRENT PRACTICE IN SEISMIC DESIGN 123 

Submerged Tunnel s 1 25 

SFBART Approach to Submerged Tunnels 128 

Japanese Approach to Submerged Tunnels 139 

Dynamic Analysis of Submerged Tunnels 1^5 

Special Design Consideration: Seismic Joint 1^8 

Underground Structures in Soil 150 

SFBART Approach to Structures in Soil 151 

Mononobe-Okabe Theory of Dynamic Soil Pressure 1 5*t 

Computer Methods for Structures in Soil 155 

Special Considerations in Design 156 

Underground Structures in Rock 158 

Design Based on Geologic Engineering Principles 1 62 

Design Based on Stress Calculations 1 66 

Special Design Considerations 170 

Underground Structures Intersecting Active Faults 171 

Case Studies of Special Design Features 171 

Recommendations for Special Design Features of 

Box Condu its 1 ~/h 

7. CRITIQUE OF THE STATE OF THE ART 177 

Effects of Earthquakes on Underground Structures 177 

Underground Seismic Motion 173 

Current Practice in Seismic Design of Underground 

Structures 179 



- mi 



CONTENTS (Continued) 



page 

Seismic Design of Subaqueous Tunnels 179 

Seismic Design of Underground Structures in Rock 180 

Seismic Design of Underground Structures in Soil 1 84 

8. RECOMMENDED RESEARCH ACTIVITIES 1 86 

Observed Effects of Earthquakes on Underground Structures 1 86 

Research Activity 1: Comprehensive Survey of 

Earthquake Effects on Underground Structures 1 87 

Research Activity 2: Postearthquake Reconnaissance 

of Underground Structures 1 88 

Research Activity 3: Observations of Selected 

Tunnels Before and After Earthquakes 1 88 

Underground Seismic Motion 1 89 

Research Activity 4: Recording of Seismic Motion 

in Deep Boreholes 192 

Research Activity 5' Recording of Seismic Motion 

in Underground Openings 192 

Research Activity 6: Development of Analytical 

Models for Predicting Seismic Motion at Depth 195 

Seismic Analysis and Design of Underground Structures 197 

Research Activity 1 \ Development of Computer Codes 

for Stability Evaluation of Openings in Rock 1 98 

Research Activity 8: Development of Empirical 

Procedures for Seismic Design 199 

Research Activity 9: Analytical Parametric Study 

of Seismic Stability of Openings in Rock 199 

REFERENCES 256 



APPENDICES 



A Persons Contacted About Seismic Design of Underground 

Structures 200 

B Abridged Modified Mercalli Intensity Scale 204 

C Summary of Damage to Underground Structures from Earthquake 

Shaki ng 206 

D A Short Review of Seismological Terms 242 

E Derivation of the Green's Function for Two-Dimens ional SH 

Motion in a Half-Space 251 



- iv - 



CONTENTS (Continued) 



page 
TABLES 

1 Possible damage modes due to shaking for openings in rock 15 

2 Test section schedule 30 

3 Summary of damage in Drift C, Shot Hard Hat J,k 

k Approximate peak values of measured free-field quantities 

versus range, Shot Hard Hat 36 

5 Compatibility of earthquake design methods with static 

design methods for openings in rock 1"Sl 



FIGURES 



1 Relation between the major tectonic plates and recent 

earthquakes and vol canoes 6 

2 Seismic zone map of the United States 9 

3 Contour map for effective peak acceleration 10 

k Calculated peak surface accelerations and associated 

damage observations for earthquakes 19 

5 Calculated peak particle velocities and associated damage 
observations for earthquakes 20 

6 Correlation of damage criteria for earthquakes and explosions 2k 

7 Damage zones from UET program 26 

8 Vertical section, Project Hard Hat 28 

9 Plan view of test sections, Project Hard Hat 29 

10 Analytical versus empirical method for estimating tunnel 

response 32 

11 Reflections and refractions of SH-waves in a horizontally 

stratified soil mass hh 

12 Typical example of the amplification function for a soil 

layer over bedrock kk 

13 Lumped-mass and spring idealization of a semi-infinite 

layered soil mass kS 

14 Axial deformation along tunnel 50 

15 Curvature deformation along tunnel 50 



- v 



CONTENTS (Continued) 



page 

16 Hoop deformation of cross section , 50 

17 Circular cylindrical cavity and incident wave 52 

18 Biaxial stress field created by a horizontal pressure 52 

19 Dynamic stress concentration factors for P-wave 53 

20 Maximum dynamic stress concentration factor K\ for 

P-wave incident upon a cylindrical cavity 55 

21 Maximum dynamic stress concentration factor K2 for 

SV-wave incident upon a cylindrical cavity 55 

22 Circular cylindrical liner and incident wave 57 

23 Maximum medium dynamic stress concentration factor Z^ 
versus liner thickness parameter v for various y and 

a (v m = v z = 0.25) 58 

2k Maximum liner dynamic stress concentration factor K-j 
versus liner thickness parameter r for various y and 
5 (v m = v^ = 0.25) 58 

25 Some wave paths between source and site regions 75 

26 Amplitude ratio versus d imens ionless depth for Rayleigh wave 79 

27 Schematic of coordinate axis, incident and reflected wave 
fronts at arbitrary angle of incidence, and surface 

control point 87 

28 Critical depth for interference of incident and reflected 

wave trains 91 

29 Displacement time histories at depth for vertically 

incident wave (e = 0°) 3h 

30 Strain component, £32, time histories at depth for 

vertically incident wave (0=0) 95 

31 Displacement time histories at depth for wave incident 

at 9 = 30° 97 

32 Strain components, £31 and £32, time histories for angle 

of incidence = 30 98 

33 Displacement time histories at the same monitoring point 

for variable angle of incidence of incoming wave 99 

3^ Strain components, £31 and £ 32 , time histories at the same 
monitoring point for variable angle of incidence of 
i ncom i ng wave 100 

35 Displacement record of the 1 966 Parkfield (California) 

earthquake monitored to below the critical depth 102 



- v 1 - 



CONTENTS (Continued) 



page 

36 Variation of peak displacement and peak acceleration 

with depth for the 1 966 Parkfield (California) earthquake \0k 

37 The cavity, coordinates, and excitation 1 06 

38 Relation between Cartesian coordinates and cylindrical 

polar coordinates 110 

39 Discretization scheme for eight points 115 

kO Effect of angle of incidence on cavity response ratio 

around the ci rcumference 1 1 6 

41 Ratio of steady-state cavity bottom response to free- 
surface response versus frequency for various depths 
and various angles of inclination 117 

hi Motion at cavity bottom and incident wave field in 

absence of cavity 119 

43 The overall design process for underground structures 124 

44 Identification of sectional and circumferential forces 127 

45 Geometry of sinusoidal shear wave oblique to axis of tunnel 129 

46 Interaction between tube and soil due to difference between 

free-field and tube displacements in SFBART approach 131 

47 Assumed geometry for determination of K g in SFBART approach 133 

48 Simple model for the analysis of circumferential bending 

due to dynamic soil pressure in SFBART approach 138 

49 Simple model for the analysis of circumferential bending 

due to inertial forces in SFBART approach 138 

50 Relative response velocity per unit acceleration 143 

51 Distribution of sectional forces by seismic deformation 

analysis and dynamic analysis 146 

52 Distribution of sectional forces by dynamic analysis using 

four different earthquake waves 147 

53 Details of seismic joint for the SFBART subaqueous tube 149 

54 Racking due to shear distortion of the soil 153 

55 Corner details for seismic design 157 

56 Seismic joint for North Point tunnel 159 

57 Cross-sectional details of drain for Marina Boulevard box 1 60 

58 Detail of vertical drain for Marina Boulevard box 1 61 

59 Tunnel stabilization system using steel sets 1 64 

60 Tunnel stabilization system using rock bolts 1 65 

- vi i - 



CONTENTS (Continued) 



page 

61 Profile for Beartrap access structure 172 

62 Typical section of Beartrap access structure 173 

63 Proposed seismic joint for reinforced concrete conduit 176 

64 Comparison of current level of development between the 

various design methods 1 82 

65 Proposed locations of triaxial accelerometers for a tunnel 19^ 

66 Proposed location of triaxial accelerometers for a large 

cavern 1 96 

67 Representation of half-space model and associated 

coordinate system 2^3 

68 Deformation due to body waves 2^5 

69 Motion due to Rayleigh waves 2^6 

70 Plane layer over a half-space 2k8 

71 Reflection and refraction of body waves 250 

72 Image source location 25^ 



- v 1 1 1 - 



Acknowledgments 

The authors gratefully acknowledge the interest and active participation of 
many persons during this investigation. Special recognition is given to those 
who conducted certain portions of the investigation under the sponsorship of 
the National Science Foundation: Arthur Carriveau for the study of dynamic re- 
sponse of underground cavities (in Chapter 5), Robert Edwards for the discus- 
sion of the nature of underground motion (in Chapter 5), Fred Kintzer for the 
section on dynamic properties of earth material (in Chapter k) , Bruce Redpath 
for the discussion of motion transducers (in Chapter 8), Peter Yanev for his 
collection of data on earthquake effects on underground structures in Japan and 
Italy, and Jack Zanetti for the parametric study of variation of motion with 
depth ( in Chapter 5) • 

Our consultants under sponsorship of the National Science Foundation were Tor 
Brekke of the University of California, Berkeley, and Donovan Jacobs and A. M. 
(Pete) Petrofsky of Jacobs Associates. They have made very valuable contribu- 
tions during the course of the work and during the review of the final report. 
Don Ross of Tudor Engineering Company reviewed the final report and offered 
many useful suggestions. 

In the course of this study, a number of individuals in many different private 
firms and government agencies have been contacted to obtain both specific and 
general information on their concerns and approaches to seismic design of un- 
derground structures. During our visit to Japan, the Japanese engineers were 
particularly helpful and informative. We wish to thank E. Kuribayashi and T. 
Iwasaki of the Public Works Research Institute, Ministry of Construction; K. 
Muto and K. Uchida of the Muto Institute of Structural Mechanics; K. Yamahara 
of The Research Laboratory, Shimizu Construction Company; and T. Ohira and T. 
Tottori of the Japan Railway Construction Public Corporation. The contribu- 
tions that these people have made to our understanding of the current state of 
the art are gratefully acknowledged. 

This report will be the primary element in the future activities of the Inter- 
national Tunneling Association's Working Group on Seismic Effects on Underground 



- ix - 



Structures. We acknowledge the interest of the group in conducting this 
study. 

Any opinions, findings, and conclusions or recommendations expressed in this 
publication are those of the authors and do not necessarily reflect the views 
of the National Science Foundation or the Federal Highway Administration. 



- x - 



Summary 

The objective of this study is to identify and evaluate the current state of 
the art of earthquake engineering of underground structures and to determine 
those areas in which additional research is most needed. Transportation tun- 
nels are emphasized in the study, but other large underground structures are 
also included. 

In recent years, new environmental requirements and population density factors 
have led to an increased interest in the exploitation of underground space for 
such diverse uses as transportation, liquid and gas storage, manufacturing, and 
disposal of hazardous materials. Simultaneously, there has been an increase in 
awareness that potentially destructive earthquakes are possible throughout most 
of the United States. Given this increased awareness of seismic hazard, it 
follows that sei smi c vu 1 nerabi 1 i ty should be considered in planning underground 
structures. 

The general view is that underground structures are much less severely affected 
by strong seismic motion than surface structures. This view is substantiated 
by the limited observations of earthquake damage to tunnels and other underground 
structures; however, some severe damage, including collapse, has been reported. 
While the seismic environment is not expected to pose a design problem, seismic 
evaluations should be conducted for most proposed critical structures such as 
nuclear power plants, liquefied petroleum gas storage facilities, and nuclear 
waste repositories for nearly all locations in the United States. In areas of 
particularly high seismic hazard, all underground projects of public importance 
should probably be investigated and engineered for seismic motion. 

EFFECTS OF EARTHQUAKES ON UNDERGROUND STRUCTURES 

A review of the past performance of 127 underground openings during earthquakes, 
including recent (1978) earthquakes, was conducted for this study. The review 
indicated that underground structures in general are less severely affected 
than surface structures at the same geographic location. While a surface struc- 
ture responds as a resonating canti levered beam, amplifying the ground motion, 



- x i - 



an underground structure responds essentially with the ground. However, the 
review showed that severe damage is often associated with tunnels in soil and 
poor rock, whereas damage to tunnels in competent rock is usually (but not 
always) minor. 

Peak ground motion parameters, such as acceleration and particle velocity, seem 
to correlate with the extent of damage. Duration of the earthquake motion also 
has an effect on the extent of damage. Besides geology and earthquake parameters, 
other important parameters that affect tunnel stability are tunnel support and 
in situ stresses. 

A thorough evaluation of the relation between these parameters and the perfor- 
mance of the underground structures was not possible because a complete suite 
of data could not be compiled. Many of the documents citing the earthquake 
performance of underground structures do not provide details on all the 
parameters. Furthermore, many of the events occurred many years ago, and it is 
no longer possible to obtain complete information on all the relevant factors. 
Consequently, at this time empirical relations between various parameters (for 
example, peak acceleration) and tunnel damage are approximate and tentative. A 
more detailed definition of the relationship requires more comprehensive studies 
than are currently available. 

VARIATION OF SEISMIC MOTION WITH DEPTH 

As an alternative to using empirical relationships to evaluate the stability of 
underground structures during earthquakes, quantitative, or numerical, analyses 
of stresses and strains can be conducted. This alternative method requires the 
characterization of seismic motion beneath the ground surface. Because motion 
is generally recorded at the surface, the question is raised as to whether the 
motion decreases with depth in some predictable manner in comparison with ground 
surface motion. Although studies of motion recorded underground tend to substan- 
tiate the idea that motion does reduce with depth, amplification at depth has 
been observed. 

There are few instances of motion recorded underground in the United States; 
however, the Japanese have approximately 200 instruments placed underground at 



-xii- 



this time. About 75% of these instruments have been placed at depths less than 
131 ft {kO m) for the purpose of studying soil-structure interaction and would 
be of little value for studying deep structures. While the data base being 
developed from these records is very useful, it is not yet sufficient to facili- 
tate a quantitative prediction of motion at depth. 

In an attempt to obtain a better theoretical understanding of the variation of 
motion with depth below the ground surface, a parametric study was conducted of 
a horizontally polarized shear wave train propagating in an elastic half-space. 
The study revealed that the incident (upward-traveling) wave and the reflective 
(downward- travel ing) wave interfere to a considerable depth, which depends upon 
the duration of the wave train. In addition, the study showed that variation 
of the peak amplitudes with depth depends on the characteristics of the wave 
train. For example, using a surface record from the 1 966 Parkfield earthquake, 
the study showed that the value of the peak acceleration was reduced to one-half 
the surface value at a depth of 200 ft (61 m) , while at a greater depth of 400 ft 
(122 m) the value was approximately three-quarters of the surface value. Conse- 
quently, peak accelerations do not necessarily reduce uniformly with increasing 
depth. Because the displacement time history is a much smoother curve than the 
acceleration time history, the values of the peak displacements reduce very 
slowly with depth. Using the record of the 1966 Parkfield earthquake, it was 
found that peak displacements reduced only about 5% at a depth of 1,000 ft 
(305 m) . Substantial reductions (on the order of k0%) were not apparent until 
very great depths of about 5,000 ft (1,524 m) were reached. 

SEISMIC WAVE STUDY OF A CIRCULAR CAVITY 

To obtain a better understanding of the seismic response of a cavity, the 
response of a circular cavity in a half-space was compared with the incident 
wave field in the half-space. For simplicity, the incident wave field was a hori- 
zontally polarized shear wave with an angle of incidence to the free surface of 
the half-space of 0°, 30°, 60°, and 90°. The depth of the cavity was taken at a 
shallow, intermediate, and great depth by considering depths of 6, 20, and 100 
times the cavity radius, respectively. In general, for cavities in hard rock 
or for cavities at great depth, it was found that the diffraction effects are 
small for the normal frequency range (say 0.1 to 15.0 Hz) of an earthquake and 



-XIII 



that the cavity response can be estimated by the incident, unscattered motion. 
However, for shallow cavities in stiff soil, it was found that there is a 
strong interaction between the cavity and the free surface and that the cavity 
response is significantly different from the incident field. 

ANALYTICAL AND DESIGN PROCEDURES FOR UNDERGROUND STRUCTURES 

Analytical procedures for predicting the response of structures to earthquake 
shaking are not as well developed for underground structures as they are for 
surface structures. The current procedures used in the seismic design of under- 
ground structures vary greatly depending upon the type of structure and the 
ground condition. 

Analytical procedures for subaqueous tunnels have been developed in both the 
United States and Japan. Procedures for submerged tunnels employ classical 
theory from the mechanics of solids and modern methods of dynamic analysis. 
Consequently, the procedures for subaqueous tunnels are fairly well formulated. 

The procedures for seismic design of structures in soil and rock are not as 
well formulated. The sophistication of stress analysis procedures ranges from 
simple calculations based upon peak ground velocity and plane wave mechanics to 
the more detailed modeling of finite-element analysis. Current static design 
practice for underground openings in rock is more strongly affected by empirical 
methods and engineering judgment during the construction phase than by stress- 
prediction models. For this reason, procedures to predict dynamic response are 
not completely compatible with current static design procedures. 

The principal concept currently in use for enhancing the seismic stability of 
underground openings is to improve the construction details so as to achieve 
better ground-support interaction. For openings in rock, this may include addi- 
tional rock bolting and reinforced shotcrete and continuous blocking of steel 
sets. Continuous blocking is automatically provided in structures that have a 
cast- in-place concrete liner. 



- xiv - 



CRITIQUE OF THE STATE OF THE ART 

From the available information on earthquake engineering of underground struc- 
tures and from the wave propagation studies conducted for this report, certain 
conclusions were drawn regarding the current state of the art: 

• The data on the effects of earthquakes on underground 
structures are not sufficient to determine the rela- 
tive importance of various parameters for predicting 
damage or lack of damage. The historical data base 
compiled for this study, although significantly larger 
than that compiled for other studies, is too small a 
base from which to draw hard and definite conclusions. 
The most important reason for the small data base is 
the apparent lack of systematic surveys of underground 
facilities following major earthquakes. 

• Data on seismic motion recorded at depth indicate a 
general trend in the reduction of peak acceleration 
with depth, although records exist of peak amplitudes 
that are greater at depth than at the surface. Many 
more records will have to be obtained at depth before 
better descriptions can emerge showing variation of 
motion amplitudes and frequency content with depth. 
The development of earthquake engineering technologies 
for underground structures will only make significant 
advances when our understanding of the underground 
motion and its effects on underground structures is 
adequately founded on observations. 

• Seismic design methodologies for subaqueous tunnels 
have been drawn from contemporary analytical tech- 
nologies and up-to-date procedures for the design of 
steel and reinforced concrete surface structures. 
Therefore, the state of the art for the seismic 
design of subaqueous tunnels appears adequate. 

• Technologies for analyzing the seismic stability of an 
opening in rock and for specifying mitigating action 
are poorly developed. The principal approaches for 
the static design of openings in rock place a great 
deal of emphasis on empirical methods and very little 
emphasis on analytical calculations for stresses. 
There has been very little effort directed toward 
developing empirical seismic analysis and design 
methods that would be compatible with the existing 
empirical static analysis and design methods. A 
method is proposed based upon a qualitative assessment 
of rock-support interaction and upon preliminary rela- 
tionships between damage to rock tunnels and peak 
ground motion parameters of earthquakes. 



- xv - 



Static design methodologies for soil tunnels are very 
similar to those for rock tunnels. In this respect, 
the relationship between static and seismic design 
methods for soil tunnels is in much the same state as 
it is for rock tunnels -- that is, the seismic methods 
are not entirely compatible with the static methods 
and are poorly developed at this time. 



RESEARCH RECOMMENDATIONS 

A number of research recommendations have been derived from this study. 
Briefly the principal recommendations are as follows: 

• Systematic reconnaissance of underground structures 
needs to be undertaken in the epicentral regions of 
recent and future major earthquakes in order to 
define empirical relationships between tunnel and 
geologic parameters and expected damage. 

• More instrumentation for recording seismic motions 
needs to be placed in tunnels and drill holes. 

• Further research is needed to better quantify under- 
ground seismic motions and to relate details of 
support enhancement to specific ground motion param- 
eters. 

• Procedures need to be further developed for the 
analysis and design of important openings in soil 
and rock. 



- xv i - 



1. Introduction 



The objective of this study is to advance the state of the art of earthquake 
engineering of transportation tunnels and other large underground structures 
by evaluating the current practice in underground earthquake engineering and 
determining those areas in which additional research is most needed. 

In the past, facilities that have been successfully constructed underground 
have included water supply and distribution systems, sanitary sewers, box 
conduits, underground passageways, tunnels, mass transit systems (including 
stations), and subaqueous tunnels. In recent years, there has been a growing 
interest in the exploitation of underground space for such uses as transporta- 
tion, liquid and gas storage, manufacturing, and disposal of hazardous mate- 
rials. With continuing improvements in construction techniques and capabil- 
ities, construction of underground facilities is rapidly expanding. Because 
of new environmental and population density factors, the underground construc- 
tion of major industrial installations is becoming more economically feasible 
and environmentally desirable. Current United States policy on the terminal 
disposal of nuclear waste is strongly directed toward burial within a repos- 
itory mined at great depth, approximately 3,000 ft (1 km). 

At the same time that construction of underground facilities is expanding, an 
awareness that potentially destructive earthquakes are possible throughout much 
of the United States is increasing. It is becoming clear that the design 
problem posed by earthquakes is not confined to California. Although under- 
ground structures are regarded as being safer than surface structures during 
strong seismic motion (a view that is, in general, supported by observed damage 
to tunnels from earthquakes), some severe damage, including collapse, has been 
reported. Verification of seismic stability will therefore be required for 
nearly all locations proposed for underground construction of sensitive struc- 
tures such as nuclear power plants, liquefied petroleum gas storage facilities, 
and nuclear waste repositories. Moreover, all underground projects of public 
importance located in areas of particularly high seismic activity should prob- 
ably be investigated and engineered for seismic motion 



- 1 - 



The work performed to achieve the objective of the present study includes seis- 
mic wave propagation analyses; a summary of observed effects of earthquakes on 
underground structures; an assessment of contemporary seismic-resistive analy- 
sis, design, and construction procedures; and an identification of future re- 
search needs. The seismic wave propagation studies consist of a review of 
theory and current approaches to inferring subsurface ground motion amplitudes 
and of numerical studies of the seismic response of an underground cavity. In- 
formation on the observed effects of earthquakes (and, to a limited extent, of 
blasts) on underground structures was obtained through a rigorous literature 
search and is used to determine the performance of various types of underground 
structures subjected to seismic motions. Contemporary seismic analysis and de- 
sign was assessed through a literature search, discussions with professionals 
in the field of underground design (see Appendix A), and an engineering evalua- 
tion of the information obtained. The report concludes with recommendations 
that identify fruitful areas of research involving both analytical studies and 
field (experimental) studies. 



- 2 - 



2. Background Information 

This report documents a study that deals with large underground structures and 
with earthquake engineering. Because these subjects are not commonly associated 
with each other in the engineering design literature (except as it relates to 
those particular structures that are part of lifelines), this chapter begins 
with a brief description of the various types of underground structures con- 
sidered in the study and the particular features of these structures that might 
be important to earthquake engineering. 

Most readers of this report are likely to be engineers who are professionally 
active in the design of tunnels and other large underground structures but who 
may have had little or no prior experience with earthquake design or earthquake 
terminology. Therefore, this chapter also includes brief discussions of seismic 
activity and earthquake hazard and of earthquake magnitude and intensity. 

UNDERGROUND STRUCTURES 

This report divides large underground structures into two major categories: 
linear structures, which are used to convey people, materials, or objects from 
one geographic point to another, and volume structures, which provide open 
spaces below ground for production facilities or storage. Linear structures 
consist of subaqueous (or immersed) tunnels, soil tunnels, rock tunnels, cut- 
and-cover conduits, and culverts. They constitute portions of transportation 
systems for motor vehicles, railroads, and mass and rapid transit. Linear 
structures also are used in the conveyance systems for liquids, primarily fresh 
water and wastewater. Underground structures that provide volume for storage 
or production facilities are usually either reinforced concrete structures with 
a shallow burial in soil (cut-and-cover construction) or caverns excavated from 
rock. Some are constructed for facilities associated with human activity; for 
example, convention halls, communication centers, recreational facilities, and 
defense installations. Other volume facilities are used as water reservoirs 
and petroleum product reservoirs and for the storage of hazardous wastes, while 
still others serve as manufacturing facilities and power plant houses. Some 
structures function as both linear and volume structures. For example, the 



- 3 



main collectors of wastewater systems that collect both sanitary sewer and 
storm water may be greatly oversized for normal daily sanitary sewer runoff in 
order to provide for temporary storage of storm-water runoff. 

The subaqueous tunnel is a unique underground structure, being quite different 
from other tunnels both in form and in construction procedures. The principal 
portion of the tunnel consists of concrete- 1 ined steel segments (sometimes re- 
inforced concrete only) that are floated into position and then sunk into 
trenches prepared in the floor of the river or bay being crossed. The seg- 
ments are joined together, the trench backfilled, and bulkheads between the 
segments removed, forming a tubular tunnel submerged in the bottom muds. Thus, 
the subaqueous tunnel is usually modeled as an elastic beam on an elastic 
foundation. 

Structures within rock and soil can be quite different from each other depend- 
ing on the strength and quality of the ground, as well as on the size of the 
opening. The rock mass can vary from very competent rock with massive blocks 
to very weak and highly fractured rock. Thus the support requirements can 
vary from no support at all to fairly heavy steel sets. Similarly, the soil 
mass can vary from a very stiff soil requiring very light steel sets to a wet, 
soft soil requiring the installation of a closed circular lining behind a 
shield. 

Regardless of the differences in the type of supports required for soil and 
rock openings, it is important to design a support that is flexible in com- 
parison with the ground. This concept is generally accepted practice in the 
design of tunnel liners for static loads. It also applies equally well to 
design for earthquake loads. The flexible support will have a good capacity 
for sustaining dynamic loads, providing its integrity is maintained during 
motion . 

The concept of flexibility is developed in liner design for soft-ground tun- 
nels. 1 It is represented by the flexibility ratio, which is the flexural stiff- 
ness of the soil medium divided by that of the liner. Thus a flexibility ratio 
greater than 1 means that the liner is more flexible than the ground. An impor- 
tant parameter in the determination of stiffness is the modulus of elasticity. 



- h - 



The stiffness of the soil varies directly with its modulus of elasticity, as 
does the stiffness of the liner. In addition, the stiffness of the liner varies 
directly with its moment of inertia and inversely with the cube of the radius 
of the opening. In general, bending moments in the liner under static loads 
increase rapidly as the flexibility ratio reduces below the value of 10. Thus 
it is desirable to design liners with flexibility ratios significantly greater 
than 1 . 

In practice, flexible support conditions are easily achieved in good rock, 
where support might consist of rock bolts or a layer of shotcrete. In less 
competent rock or soil, where thick liners are required, it is both possible 
and desirable to achieve a flexible liner. 

SEISMIC ACTIVITY AND EARTHQUAKE HAZARD 

The following brief discussion is intended to provide the newcomer to the field 
of earthquake engineering with some of the basic concepts associated with seismic 
hazards. It is not intended to be complete or thorough. For more detailed in- 
formation on the relevant aspects of seismology, the reader is referred to the 
general 1 i terature. 2 > 3 > 4 > 5 

The subject of seismicity addresses the spatial distribution of earthquakes as 
well as their frequency of occurrence. Most earthquakes occur at the boundaries 
of the major tectonic plates, as shown in Figure 1, and are due to the relative 
motion between these plates. The San Andreas fault in California delineates 
part of the boundary between the North American Plate and the Pacific Plate. 
Earthquakes generated along this fault result from the northwesterly movement 
of the Pacific Plate relative to the North American Plate as these two plates 
slide past each other. At some boundaries, two plates have a relative motion 
toward each other. If one plate is an oceanic plate and the other is a conti- 
nental plate, the oceanic plate slides underneath the continental plate in a 
process referred to as subduction. This phenomenon is typical of the plate 
boundaries along Japan, south of Alaska, and along the western coast of South 
America. If the two plates in relative motion toward each other are both con- 
tinental masses, neither plate is subducted. Instead, the two plates collide, 
and mountain ranges are pushed up along the boundary. The most active boundaries 

- 5 - 




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- 6 



are those between converging plates, as described above. Boundaries between 
diverging plates, marked by spreading ridges, are relatively inactive. 

In the interior of tectonic plates, the frequency at which earthquakes occur 
is much less than along the plate boundaries, although, even in these areas, 
major destructive earthquakes do sometimes occur. The central and eastern 
portions of the United States are not as seismically active as the western por- 
tions, particularly California; however, several major earthquakes have occurred 
in these midplate regions of the North American Plate in the recent past. Two 
moderately large earthquakes occurred off Cape Ann, Massachusetts, in 1638 and 
1755. A series of three extremely large earthquakes occurred near New Madrid, 
Missouri, in 1 8 1 1—12 and were felt as far away as Washington, D.C. Another 
major eastern event was the destructive earthquake at Charleston, South Carolina, 
in 1886. Neither of these large earthquakes nor the many shocks of moderate 
size in the eastern and central regions of the United States can be explained 
by interaction between tectonic plates. 

In assessing earthquake hazards, one of the main distinctions between the eastern 
and western regions of the United States is the degree of difficulty encountered 
in identifying and mapping active faults. In the western United States, earth- 
quakes can usually be associated with active faults, which in general have been 
readily identified and mapped. However, in the eastern and central United 
States, it has not yet been possible to associate earthquakes in general with 
known faults. Geologic history seems to have obscured the faults in these 
regions so that it is much more difficult to identify and map active faults. 
Furthermore, relatively few earthquakes have occurred in the eastern United 
States, making prediction of both spatial distribution and frequency of occur- 
rence much more difficult there than in the western region. 

Although major earthquakes in the eastern United States appear to be infrequent 
and are more widely dispersed than those in the western United States, the ques- 
tion remains: can damaging earthquakes such as those of 1755, 1811-12, and 
1886 occur anywhere in the eastern North American continent? The importance 
of intraplate earthquakes has only recently begun to receive attention, and 
many valuable studies, such as those by Sykes 6 and Bollinger, 7 are being con- 
ducted. The historic record of earthquakes in the eastern United States spans 



- 7 - 



less than 300 years, and Bollinger suggests that that is not a long enough 
period from which to deduce the presence or absence of a cyclical behavior of 
earthquakes in the region. In support of this view, Bollinger points to the 
work of Ambraseys 8 on damaging earthquakes over a period of 2,000 years for the 
Istanbul region in northeastern Turkey and for the Anatolian fault zone in 
northern Turkey. Both of these regions have experienced quiescent periods of 
up to several hundred years followed by long periods of intense earthquake 
act i vi ty. 

By studying regional seismicity, the comparative earthquake hazard for various 
locations can be determined. Qualitatively, this is expressed in the form of 
a seismic zone map in the Uniform Building Code , 9 as illustrated in Figure 2. 
A better indication of seismic hazard would be gained by expressing it in the 
form of the odds that an earthquake that produces peak ground acceleration ex- 
ceeding a given value within a given period of time will occur at a certain 
site. Such a probabilistic expression of seismic hazard was used to prepare a 
new seismic hazard map of the United States for the Applied Technology Council. 10 
This map, shown in Figure 3, indicates the effective peak acceleration (EPA) 
that might be expected to be exceeded during a 50-year period with a probability 
of 1 in 10. Although, at present, EPA does not have a precise physical defini- 
tion, it is related to the smoothed elastic response spectrum in this way: the 
5%-damped spectrum for the actual motion is drawn and fitted with a straight 
line between the periods of 0.1 and 0.5 sec; then the ordinate of this straight 
line is divided by 2.5 to obtain EPA. 10 Bolt suggests that EPA "can be thought 
of as the maximum acceleration in earthquakes on firm ground after high fre- 
quencies that do not affect sizeable structures (large houses, factories, 
bridges, dams, and so on) have been discounted.' 

It is extremely important to note that both these seismic hazard maps are based 
upon seismic history only. This may be inadequate because the distribution of 
active faults has not been considered and because some of these active faults 
have not produced activity during the relatively short historical observation 
period. 



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- 10 - 



EARTHQUAKE MAGNITUDE AND INTENSITY 

Because the Richter scale is widely used to describe the size of earthquakes, 
a few brief comments about the significance of the scale and its general rela- 
tionship to the severity of ground motion are given here for the benefit of 
those outside the earthquake engineering field. Basically, a value on the 
Richter scale logarithmically represents the amount of energy released by the 
event. An increase of one unit on the scale represents approximately a 30-fold 
increase in the energy released. An earthquake is generated by the rupture of 
rock and slip along a fault in the earth's crust. Sometimes surface rupture 
occurs and delineates the fault. Generally, the larger the magnitude (M) , the 
greater the length of rupture. This means that usually a greater length of a 
fault will slip during a large-magnitude event than during a small one; con- 
versely, a longer fault can produce a larger magnitude earthquake. 

The experience of strong ground motion at a particular site is of course related 
to the Richter magnitude; however, distance from the source and the local site 
conditions are also factors that affect the ground motion at the site. As 
earthquake waves propagate from the source, they attenuate with distance. This 
relationship has been investigated and presented in the form of attenuation 
curves, such as those given by Schnabel and Seed, 11 Idriss, 12 and Blume. 13 
Because the source of motion is not a point but rather is distributed along a 
long section of a fault, the severity of ground shaking at a site close to a 
fault may not change greatly as a function of magnitude. As an example, con- 
sider the transbay tube of the San Francisco Bay Area Rapid Transit District, 
located in San Francisco Bay between the cities of San Francisco and Oakland, 
California. The following rather interesting discussion of the earthquake 
considerations for the design of the tube is given by Housner: lt+ 

A great earthquake ... is very likely to occur on the San 
Andreas fault as it did in 1906. That earthquake is esti- 
mated to have had a Richter magnitude of 8.25 and slipping 
occurred along a length of fault of some 200 miles with the 
maximum relative offset of the two sides of the fault reach- 
ing approximately 20 feet in the neighborhood of Tomales 
Bay. The ground motion produced in the general bay area 
by the 1 906 shock is judged to be equal to the most intense 
motion likely to be produced by any future earthquakes. If 
an earthquake larger than the 1 906 shock were to occur, say 
one having magnitude 8.6, this would mean that the length 



- 11 - 



of the fault along which slipping had occurred was somewhat 
greater than in the 1 906 shock and these increments of ex- 
tra slipping would be at distances of one hundred miles or 
more from the tube location and hence would have a negli- 
gible effect upon the intensity of ground motion at the 
proposed site of the tube. In fact, the length of slipping 
associated with a magnitude 7 shock (approximately fifty 
miles) is sufficiently great so that the intensity of ground 
motion at the tube site can be expected to be almost as 
severe as during an earthquake of 8.25 magnitude. This 
point is emphasized to call attention to the fact that it 
is not necessary to wait for an extreme earthquake (magni- 
tude 8 or greater) in order to experience extreme ground 
motion. 



Another way of describing the size of an earthquake is by means of intensity 
scales that are related to the amount of damage to buildings and other man- 
made structures, to the extent of the reactions of animals and people, and 
to the degree of disturbance to the ground. Intensity is not always directly 
related to magnitude because it is a function of other parameters as well -- 
in particular, local soil conditions and the distance from the epicenter. 

The Rossi-Forel scale, the first intensity scale of modern times, ranges in 
value from I to X. It dates back to the 1880s and was used to describe the 
intensities of the 1906 San Francisco earthquake in the published reports 
immediately following that event. The Rossi-Forel scale has been largely 
replaced by the Modified Mercalli Intensity (MM I ) scale, which ranges in value 
from I to XII. The original Mercalli Intensity scale was modified by Richter 
in 1 956 , 4 but a newer version has been developed by Wood and Newmann to repre- 
sent more contemporary construction practices. 2 This newer version, called 
the abridged Modified Mercalli Intensity scale, is given in Appendix B. Note 
that all structural references in the appendix are for surface structures and 
that there are no references to underground structures. 



- 12 - 



3. Observed Effects of Earthquakes and Underground Explosions 

This chapter summarizes the effects of earthquakes and subsurface blasts on 
large underground structures. Much of the information presented here was 
obtained from published reports. Primary attention is given to the effects 
of earthquakes; however, the effects of underground conventional and nuclear 
explosions are also included. 

The term large underground structure denotes transportation tunnels, mines," 
underground power plants, aqueducts, and utility tunnels. Although submerged- 
tube transportation tunnels are large underground structures, they are usually 
fairly rigid compared with the surrounding medium and behave much differently 
than tunneled or mined structures in rock and firm soils. Consequently, sub- 
merged tunnels are excluded from this review. Because information regarding 
cut-and-cover structures is sparse, only a brief discussion of those structures 
is possible in this report. 

EFFECTS OF EARTHQUAKES 

The effects of earthquakes on tunnels, mines, and other large underground 
structures have been summarized in several reports. 15-18 Duke and Leeds 
presented one of the early evaluations of earthquake damage to tunnels. 15 
Stevens reviewed the effects of earthquakes on mines and other underground 
openings. 15 Dowding and Rozen studied the response of rock tunnels to earth- 
quakes and correlated the damage to peak ground motion. Additional informa- 
tion was obtained from other sources. 19-33 

Earthquake damage to underground structures may be attributed to three factors: 

• fault slip 

• ground fai lure 

• shaking 



'It is recognized that mines are different from underground, civil-engineered 
structures; however, mines yield useful information on seismic response. 



- 13 - 



Damage due to sudden fault slip has been reported in tunnels where the opening 
passes through a fault zone. The damage varied from minor cracking of the tun- 
nel lining to collapse and closure of the opening. Usually damage was restricted 
to the fault zone. Clearly, fault slip cannot be prevented; therefore, the only 
way to avoid this damage is to avoid intersecting an active fault. When this 
is not possible, fault slip damage is to be expected, and postearthquake repairs 
should be planned in advance. 

Ground failures, such as rock slides, landslides, squeezing, soil liquefaction, 
and soil subsidence, have damaged portals and shallow structures. Sometimes 
slides from slopes adjacent to tunnel portals have closed tunnels while doing 
little or no damage to the portal. More often, slides have caused severe damage 
to the portals when the rock and soil around the portal have been involved in 
the slides. Shallow structures in steep terrain may also be affected by slides. 
For example, a major section of a highway tunnel in the Izu Peninsula, Japan, 
was removed by a landslide during the Near Izu-Oshima earthquake of January 14, 
1978. Damage due to ground failure may be avoided by careful siting and attention 
to slope stabi 1 i ty. 

Effects of shaking deserve special attention. It should be noted that ground 
failure induced by shaking can cause damage to the structure indirectly, without 
the shaking itself causing damage. This discussion is centered on damage to 
underground openings caused directly by shaking. Possible modes of damage due 
to shaking are listed in Table 1. Possible secondary consequences of these 
damage modes are also indicated. 

Response Parameters 

Information about the underground structure and about the earthquake is needed 
to evaluate damage due to earthquake shaking. The parameters that influence 
the earthquake response of underground structures are: 

Cross-sectional dimensions (shape and size) 
Depth of structure below the ground surface 
Type, strength, and deformabi 1 i ty of rock or soil 
Support and lining systems 
Shaking severity (intensity, peak ground motion) 



- 14 - 



Table 1. Possible damage modes due to 
shaking for openings in rock. 



Possible Damage Mode 


Possible Consequence 


Rock fal 1 


Injure personnel 

Block transportation 

Block venti lat ion 

Disrupt water management 
and other services 

Damage equipment 

Damage shaft wal 1 


Rock slabbing 


Same as for rock fall 


Existing rock fractures and 
seams open up, rock blocks 
shift 


Increase permeability 
along the opening 

Weaken rock structure 


Cracking of concrete liners 


Increase permeability 
Weaken 1 iner 


Spalling of shotcrete or 
other surfacing material 


Lead to rock fal 1 if 
extens i ve 


Unraveling of rock-bolted 

system 


Same as for rock fall 


Steel set col lapse 


Same as for rock fall 



- 15 - 



The values of the in situ stresses at the depth of the underground structure 
are very important for the seismic evaluation of the structure. Unfortunately, 
it is extremely difficult to obtain reliable data on in situ stresses; however, 
the stresses can be estimated using empirical relations that associate with 
depth. Therefore, the depth of the structure below the ground surface is the 
desired parameter from a practical point of view. 

The types of support that are found include rock bolts (sometimes with wire 
mesh), steel sets, shotcrete, and concrete (or even brick) lining, alone or in 
combination; in some cases, no support at all is used. Ground conditions may 
be characterized mainly by the type, strength, and deformabi 1 i ty of the rock or 
soi 1 . 

The severity of the earthquake shaking at the site of the underground structure 
may be represented simply by an intensity scale or by peak ground motion param- 
eters. It would be most appropriate to have information on shaking at the 
depth of the opening; however, data are usually available only for shaking at 
the ground surface or not at all. 

Summary of Available Data 

Information concerning damage to tunnels, mines, and other underground openings 
from earthquake shaking is summarized in the table that makes up Appendix C. 
The table was constructed using data obtained from Stevens, 16 Dowding and Rozen, 17 
and many other sources. 19-33 Of the 127 cases cited, cases 1 through 71 coincide 
with the cases studied by Dowding and Rozen. 17 * 2lf 

Appendix C identifies each case by the name of the earthquake and the name of 
the tunnel, mine, or underground opening. General information about the earth- 
quake, such as date of occurrence, magnitude (M) , and duration (D) , may be pro- 
vided along with the earthquake name. The table summarizes available data 
concerning the opening, the shaking at the ground surface, and the shaking 
underground. The important factors influencing the earthquake behavior of 
underground structures are represented by individual columns in the table. 
Completion of all columns for each case was not possible because of data 
limitations and time constraints; however, the columns do present the data 



- 16 - 



on the opening and the shaking that are needed to properly evaluate possible 
underground structural damage and to correlate that damage with ground motion. 
It is hoped that, following future destructive earthquakes, all such informa- 
tion on openings in the epicentral regions can be assembled by reconnaissance 
teams. 

It should be noted that the reporting of portal damage in Appendix C differs 
somewhat from the method used by Dowding and Rozen, 17 > 2i+ who reported all 
portal damage under the heading "damage due to ground failure and other 
reasons" as separate from damage due to shaking and fault movement. Inspection 
of some of the data sources revealed that some portal damage could not be directly 
attributed to landslides or to other types of ground failure. It is quite likely 
that, unless ground failure or faulting was indicated, portal damage was prob- 
ably due to shaking alone. Therefore, if the actual cause of the portal damage 
was not reported, that damage is reported in Appendix C as having been due to 
shaking. 

Peak Ground Motion Parameters . Peak ground motion parameters reported in 
Appendix C for cases 1 through 71 were obtained from Rozen, who calculated 
them for a ground surface location above each tunnel using an empirical predic- 
tion procedure. 24 The reader should be careful in regarding these values as 
accurate, or even approximate, representations of ground motions at the sites. 
The procedure employed by Rozen required using the distance from the epicenter 
to the site. Values calculated in this manner may be misleading when the site 
is adjacent to the ruptured fault. For example, Wright Tunnel No. 1 and No. 2 
were approximately 84 miles (135 km) from the epicenter of the 1906 San Francisco 
earthquake, and Rozen predicted a peak acceleration of 0.1 3g* at these sites 
(cases 1 and 2). However, the actual peak acceleration must have been signifi- 
cantly higher because the San Andreas fault intersected Wright Tunnel Mo. 1 and 
created an offset in that tunnel of 4.5 ft (1.4 m) . Therefore, it appears 
that Rozen simply used the distance from the site to the epicenter rather than 
the shortest distance to the ruptured fault, the latter being the more appro- 
priate procedure. 



>g is a constant representing acceleration of gravity equal to 32.2 ft/sec 
(981 cm/sec 2 or 981 Gal) 

- 17 - 



Another reason for regarding Rozen's predictions of the peak ground motions as 
approximate values is that a given attenuation relation cannot be applied to 
all earthquakes or to all site conditions. The selection of an appropriate 
attenuation relation for a given earthquake and a given site requires careful 
consideration of seismological data. Relations other than the one used by 
Rozen may result in very different predicted values. To illustrate this point, 
let us consider specific tunnels for two different earthquakes — the 1 964 
Alaska earthquake and the 1971 San Fernando earthquake. For Whittier Tunnel 
No. 1 and No. 2 (cases 39 and 40) , located k~] miles (75 km) from the epicenter 
of the Alaska earthquake, Rozen predicted a peak acceleration of 0.26g. However, 
an attenuation relation from the Offshore Alaska Seismic Exposure Study, which 
should be a much more appropriate reference, yields a much lower value of 0. 1 4g. 3Lf 
A relation by McGuire predicts a much higher value of 0.35g. 35 The relation is 
based upon western United States data and may not be appropriate for the Alaska 
setting. In the example of the San Fernando earthquake, consider first the 
Tehachapi Tunnels (cases 53 and 5*0 , which are located 45 miles (73 km) from the 
epicenter. The McGuire relation happens to yield a value of 0.07g. 35 The value 
was predicted by Rozen; however, the SAM V relation by Blume yields a lower 
estimate of 0.04g. 13 Tunnels closer to the epicenter are even more interesting 
with regard to the diversity of predicted values. Consider several tunnels 
(cases 47, 48, and 49) located 10 miles (16 km) from the epicenter. For these 
tunnels, the Blume relation agrees with the 0.23g predicted by Rozen, while an 
attenuation relation developed specifically from the San Fernando earthquake by 
Duke et al. estimates a much larger value of 0.36g. 36 Clearly, the use of attenu- 
ation relations to estimate peak ground motion parameters requires careful con- 
sideration of the location of the earthquake, the type of earthquake source, and 
the characteristics of the ground at the site. 

Figures 4 and 5 summarize the correlations of observed damage to peak accelera- 
tions and to peak particle velocities at the surface as prepared by Dowding and 
Rozen. 17 Three damage levels due to shaking were identified. The classification 
no damage means no new cracks or fall of rocks, minor damage includes new crack- 
ing and minor rockfalls, and damage includes severe cracking, major, rockfalls, 
and closure. 



- 18 - 



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Damage 



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LEGEND 

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oMinor damage, due to shaking 

^Damage from shaking 



p a Near portal 
s a Shal low cover 



Figure k. Calculated peak surface accelerations and 
associated damage observations for earthquakes. 
(Adapted from Reference 17.) 



19 



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Figure 5- Calculated peak particle velocities and 
associated damage observations for earthquakes. 
(Adapted from Reference 17.) 



- 20 



Cut-and-Cover Structures . Shallow structures constructed in soil (or soft rock) 
by cut-and-cover procedures form a unique class of underground structures that 
deserves special attention. Previous studies of the effects of earthquakes on 
underground structures have emphasized openings mined from rock. Dowding and 
Rozen emphasized rock tunnels in their studies but included a few soil 
tunnel s , 17 ' 2i+ while Stevens discussed only mines. 16 A few reports of damage 
to cut-and-cover structures were documented from other reports, however. Case 
115 in Appendix C involves a cut-and-cover railroad tunnel destroyed by the 
1906 San Francisco earthquake. Cases 121 through 126 report damage to cut-and- 
cover conduits and culverts during the 1971 San Fernando earthquake, and case 
127 reports damage from the same earthquake to a large buried reservoir. 
Although there may be many more such structures, both damaged and undamaged 
by strong earthquake motion, their documentation would be time consuming and 
was not possible for this study. 

The sample of cut-and-cover structures available for this report is too small 
to provide firm conclusions; however, some observations are possible. Much of 
the damage may be attributed to large increases in the lateral forces on buried 
structures from the soil backfill during seismic motion. This would account for 
racking of structures and damage to walls, including failure of longitudinal 
construction joints, development of midheight longitudinal cracks, and formation 
of plastic hinges at the top, midheight, and bottom of walls. Structures with 
no moment resistance, such as the unreinforced brick arch of case 115, are 
susceptible to collapse under the dynamic action of the soil backfill. As with 
surface structures, the extent of the damage in shallow buried structures may 
depend greatly upon the duration of the strong shaking. Damage initially 
inflicted by earth movements, such as faulting and landslides, may be greatly 
increased by continued reversal of stresses on already damaged sections. 

Conclus ions . The following conclusions may be drawn from the data presented in 
Appendix C: 

• Little damage occurred in rock tunnels for ground sur- 
face accelerations below 0.4g. Dowding and Rozen 
found that there was no damage in either lined or 
unlined tunnels for ground surface accelerations up 
to 0.19g. They found a few cases of minor damage, 
such as falling of loose stones and cracking of brick 



- 21 - 



or concrete linings, for ground surface accelerations 
above 0.1 9g and below 0.4g. (For reasons noted above, 
these values of accelerations must be regarded as 
approximate and tentative.) 

Severe damage and collapse of tunnels from shaking 
occurred only under extreme conditions. Dowding and 
Rozen observed that no collapse occurred for ground 
surface accelerations up to 0.5g. Severe damage to 
the lining or portals from strong shaking was usually 
associated with marginal construction, such as brick 
or plain concrete liners and the lack of grout between 
wood lagging and the overbreak. Poor soil or incom- 
petent rock also seemed to contribute to the suscepti- 
bility of tunnels to damage. 

Severe damage was inevitable when the underground 
structure was intersected by a fault that slipped 
during the earthquake. 

Instances of complete tunnel closure appeared to be 
associated with movement of an intersecting fault and 
with other major ground movements, such as landslides 
and liquefaction, but not with shaking alone. 

Dowding and Rozen concluded that tunnels were much 
safer than aboveground structures for a given inten- 
sity of shaking. Only minor damage to tunnels was 
observed in areas subjected to MM I VIII to IX, 
although damage to surface structures at these 
intensities is usually extensive. 

There was some evidence that tunnels deep in rock were 
safer than shallow tunnels, although the data providing 
this evidence were incomplete. 

Damage to cut-and-cover structures appeared to be 
caused mainly by large increases in the lateral forces 
from the surrounding soil backfill. 

Duration of strong seismic motion appeared to be an 
important factor contributing to the severity of 
damage to underground structures 



EFFECTS OF UNDERGROUND EXPLOSIONS 

The effects of explosion- induced ground vibrations on underground openings are 
reported in several different contexts. Conventional blasting, as used in 
mining and underground excavation, constitutes the most common source of 
explosion- induced vibration. Other sources are high explosives and underground 
nuclear explosions (UNEs) used in connection with national defense studies. 
The ground motions from these three sources differ from earthquake ground motions 



- 22 - 



(and to a certain extent from each other) in frequency content, values of peak 
ground motion parameters, and duration. For example, low-cycle fatigue failure 
of rock may be an important causative influence in some ground motion effects; 
but fatigue failure is dependent on the number of stress cycles, which, in turn, 
depends upon the frequency content and duration of the blast- or earthquake- 
induced waves. Valuable insights are obtained by studying the effects of under- 
ground explosions. 

Conventional Blasting 

Langefors and Kihlstrom suggest particle velocity criteria for damage to unlined 
rock tunnels during blasting operations. 37 A particle velocity of 12 in. /sec 
(30.5 cm/sec) causes rock to fall in unlined tunnels, and that of 2k in. /sec 
(61 cm/sec) results in the formation of new cracks in the rock. Bauer and 
Calder relate damage from blasting vibrations to particle velocity as follows: 38 

• less than 10 in. /sec (25 cm/sec) - no fracturing of 
intact rock 

• 10 to 25 in. /sec (25 to 6^ cm/sec) - minor tensile 
slabbing 

• 25 to 100 in. /sec (6*t to 25*t cm/sec) - strong tensile 
cracking, some radial cracking 

• over 100 in. /sec (25^ cm/sec) - complete breakup of 
rock mass 

These criteria correlate well with the peak particle velocity thresholds for 
earthquakes suggested by Dowding and Rozen that are illustrated in Figure 6. 

Dowding and Rozen reviewed an experiment conducted at the Climax, Colorado, 
mine of AMAX to investigate cracking of shotcrete liners caused by explosion- 
induced vibrations. 17 The tunnels were rock bolted and lined with 2 to 11 in. 
(5 to 28 cm) of shotcrete. Dowding and Rozen reported that formation of hair- 
line cracks in the shotcrete liner occurred at peak particle velocities of 
approximately 36 in. /sec (91 cm/sec), and faulting of cracks, which evidently 
means shearing of existing cracks, at approximately *t8 in. /sec (122 cm/sec). 

High-Explosive Tests 

Similar results were obtained for rock tunnels in the underground explosion 
tests (UET) conducted by Engineering Research Associates for the U.S. Army 



- 23 - 



150 — 



100 — 






CO 



50— 
40- 
30- 

20- 
10- 



damage 
32 



minor 
damage 



no 
damage 



earthquake 
cri teria, 



Dowd i ng 
and Rozen 



format ion 
of new 
cracks 



\ 



fall of 
rock in 
un 1 ined 
tu nnels 
12 



\ 



-100- 



Zone 3 
damage 

156 



blasting 
cri teria, 



Langefors 

and 

| Ki hi strom 



strong 
tensi le 
and some 
radial 
cracking 

25 



shearing 
of cracks 
in 
shotcrete 

-k8 *- 

ha i rl ine 
cracks in 
shotcreteV 
36 *- 



minor 
tens i le 
slabbing 



10 

no fracture 
of intact 
rock 



blasting 
cri teria, 



Bauer 

and 

Calder 



(shotcrete- 
1 ined 
tunnels) 



AMAX 
tests , 



Dowding 
and Rozen 



Zone k 

damage 



36 



no 

damage 



(unl ined 
tunnels) 



UET 



Hendron 



average 
va 1 ue 
for UET 
damage V 
48 -*- 



1 owe s t 
value 
for UET 
damage 
18 



(un 1 ined 
tunnel s) 



approximate 
threshold 
of Zone 3 
damage 

■132-5 



approx i mate 
threshold 
of Zone k 
damage 

n-± 



no 

damage 



UET 



Dowd i ng 
and Rozen 



(un 1 ined 
access 
tunnel ) 



Hard Hat 
test 



NOTE 



1 in. /sec = 2.5^ cm/sec. 



Figure 6. Correlation of damage criteria for earthquakes and explosions, 



- 2k - 



Corps of Engineers. 39 These tests studied the damage to unlined tunnels in 
sandstone, granite, and limestone due to TNT explosions. Diameters of the 
tunnels varied from 6 to 30 ft (1.8 to 9 m) , and the charge varied from 320 
to 320,000 lb (145 to 145,000 kg). Four zones of failure were identified in 
the UET program, as illustrated in Figure 7. Zone 1 represents heavy damage 
with tight closure of the tunnel. Damage in Zone 2 is also very heavy, but it 
decreases with distance from the explosion. Zone 3 represents a length of con- 
tinuous damage to the tunnel surface toward the charge and intermittent spalling 
around the rest of the tunnel. Damage in Zone 4 consists of intermittent spall- 
ing of rock that may have been loosened by the excavation process. Beyond Zone 4, 
there is no damage. The peak particle velocities associated with the boundaries 
of Zone 4 are of particular interest because they indicate thresholds for minor 
damage (such as falling of loose rock) as well as for major damage. Hendron 
analyzed the UET results and found that the outer limit of Zone 4 corresponded 
to a particle velocity (radial with respect to the explosion) of 36 to 72 in. /sec 
(91 to 183 cm/sec) and that the outer limit of Zone 3 corresponded to a particle 
velocity of 1 56 in. /sec (396 cm/sec). 40 Hendron also noted that the free-field 
radial strains corresponding to the outer limits of these two zones were 0.0004 
for Zone 4 and 0.0012 for Zone 3. Dowding and Rozen further investigated 
Hendron's data on the outer limit of Zone 4 and found that, although the particle 
velocity of one of the 14 tests may have been as low as 18 in. /sec (46 cm/sec), 
the average particle velocity was 48 in. /sec (122 cm/sec). 17 These values for 
particle velocity from the UET program are shown in Figure 6 for comparison with 
results from other studies. 

The final report 39 on the UET program makes the following comments regarding 
protection against damage: 

There is some evidence from these tests regarding the type 
of structure which would protect a tunnel installation 
against damage to tunnels. While this evidence is meager, 
it does indicate that reflecting surfaces could be used 
to turn back much of the energy. In a few cases geological 
conditions provided such surfaces, and the damage beyond 
them was considerably reduced. This could well afford the 
basis for protective design by tunnel liners with reflecting 
surfaces. The following comments represent rough estimates 
which should be tested experimentally. 

The damage which occurs in Zone 4 and some of that in Zone 3 
is inferred to consist of the dislodgement of rock fragments 



- 25 - 







Zone 1 



Tight Closure 



Tunnel 



Zone 2 



General 
Fai lure 



Zone 3 



Local Failure Intermittent 
Fai lure 



Zone k 



Hendron, "Engineering of Rock Blasting on Civil Projects", 
in Structural and Geoteohniaal Mechanics, edited by W. J. Hall, 
©1977, p. 256. Reprinted by permission of Prentice-Kail, Inc. 
Englewood Cliffs, New Jersey. 



Figure 7- Damage zones from UET program. 
(Adapted from Reference kO. ) 



- 26 - 



which have been partially separated from the main body of 
the rock by blasting or by weathering. ... A simple con- 
crete lining placed in contact with the rock might prove 
effective in protecting against this kind of damage. 

In Zone 3 damage, solid rock is cracked and slabs fall 
off. ... A substantial lining is required which should 
not make contact wi th the rock. The space between the 
lining and the tunnel surface should be filled with a 
material of low density that will absorb the energy of 
the flying rock, distribute the pressure from fallen rock, 
and provide a mismatch of acoustic impedance so that re- 
flection will take place at the tunnel surface rather than 
at the surface of the lining. 

Underground Nuclear Explosions 

Tests on tunnel damage have also been conducted in conjunction with 
UNEs. Various tunnel cross sections and liners were tested during the shot 
Hard Hat (February 1962) in the Climax granite at the U.S. Department of 
Energy's Nevada Test Site. 41 Extensive tunnel tests were also performed in 
connection with Project Piledriver, but those reports are not declassified 
as yet and cannot be summarized here. 

Tunnel Test Sections . The Hard Hat tunnel experiments consisted of k"$ tunnel 
sections with varying cross sections, liners, and backpacking. These test 
sections were distributed among three test drifts (A, B, and C) with increasing 
distance from the zero point of the explosion. The layout for the tunnel tests 
is illustrated in the vertical section of Figure 8 and the plan view of Figure 9- 
The elevator shaft, access tunnel, and test drifts were excavated through reason- 
ably competent quartz monzonite. 

The variations in cross section, liner, and backpacking are presented in Table 2. 
Test sections with circular cross sections and others with square cross sections, 
some unlined (unsupported) and some lined simply with rock bolts and wire mesh, 
were located in Drifts B and C. Horseshoe-shaped sections supported by steel 
sets with wood lagging, familiar in civil and mining projects, were also located 
in Drifts B and C. Circular sections lined with reinforced concrete cast against 
the rock were constructed in all three drifts. The remaining 30 sections were all 
circular, with backpacking between the liners and the rock. The various combina- 
tions of liners and backpacking can be summarized in several general categories as 
fol lows: 

- 27 - 



LTV 



Surface 




z 



3-ft Cased Hole 
(Station U15a) 



£ 



800 ft- 



-A\A- 



Jj] 

1 
i 



Elevator Shaft 
(Station 1500) 



Test Drift A 



Elevation of 
jj Test Drift A 

f 



Test Drift B 



Test Drift C I 




^ 4' % GRAPE 



T i vo u n a u c 

iiteiifeiii m& 



Zero Point 



Access Tunnel 



NOTE 



1 ft = 0.30A8 m. 



LTV 
0O 



Figure 8. Vertical section, Project Hard Hat. 
(Adapted from Reference k\.) 



- 28 - 



Test Drift B 



Test Drift C 



Abandoned 
Test Drift 




Figure 9. Plan view of test sections, Project Hard Hat, 
(Adapted from Reference *»1 . ) 



- 29 - 



Table 2. Test section schedule. (Source: Reference 41.) 





Test 


Sect 


'on 


Shape 


Liner Type 


Backpacking 


Drift 


Number 




B 


C 


la 


□ 


Unl ined 


None 




B 


C 


lb 


□ 


Lined with rock bolts 
and wi re mesh 


None 




B 


C 


2a 


O 


Unl ined 


None 




B 


C 


2b 


O 


Lined with rock bolts 
and wi re mesh 


None 


A 


B 


C 


3a 


o 


Reinforced concrete 


None 


A 


B 


C 


3b 


o 


Reinforced concrete 


Foam 


A 


B 


C 


3c 


o 


Reinforced concrete 


Foam 


A 


B 


C 


3d 


o 


Reinforced concrete 


Cinder 


A 


B 


C 


ka 


o 


Steel set wi th 
steel lagging 


Cinder 


A 


B 


C 


kb 


o 


Steel set with 
steel lagging 


Foam 


A 


B 


C 


kc 


o 


Steel set wi th 
wood lagging 


Foam 


A 


B 




5a 


o 


3-gage steel 


Foam 


A 


B 




5b 


o 


3-gage steel 


Foam 


A 


B 




5c 


o 


3-gage steel 


Cinder 




B 


C 


6a 


o 


8-gage steel 


Foam 




B 


C 


6b 


o 


8-gage steel 


Foam 




B 


C 


6c 


o 


8-gage steel 


Cinder 




B 


C 


7a 


A 


Steel set and 
wood lagging 


None 



- 30 - 



• Categories of liners with backpacking 

— Flexible - 8-gage or 3~gage corrugated steel 

— Rigid - 8-in. (20-cm) or 12-in. (30-cm) reinforced 
concrete 

-- Intermediate - steel rings or horseshoe-shaped sets 
with wood or steel lagging 

• Categories of backpacking 

-- Thick filler - 20 in. (51 cm) or 2k in. (61 cm) of 
polyurethane foam 

— Thin filler - 5 in. (13 cm) or 9 in. (23 cm) of 
polyurethane foam or 9 in. (23 cm) of volcanic 
cinder 

Preshot estimates of tunnel response were made assuming a 5-0-kiloton (*t.5-kt) 
device. A simple analytical procedure based on wave theory was used to esti- 
mate limits of compression failure, tensile splitting, and spalling (or scabbing) 
In addition, an empirical approach derived from the UET program and previous UNE 
tests was employed to estimate damage zones. These estimates are illustrated in 
Figure 10. 

The actual yield of the Hard Hat device was 5-9 kiloton (5.^ kt) . Postshot 
determinations of the actual point of closure and the actual limits of Zones 2, 
3, and k were made along the unlined access tunnel as indicated in Figure 10. 
Drift A was tightly closed, and most of the data were unrecoverable. Drift B 
was well within the closure zone, although preshot estimates placed it beyond 
closure at the limit of Zone 2. Many of the intended results of Drift B were 
lost, but some observations were possible. Drift C also sustained heavier 
damage than planned; however, the test sections there provided some interesting 
results. 

Damage Data . Some damage to the elevator shaft was observed at all depths, but 
damage was heavier in the upper half than in the lower half. Damage consisted 
of permanent misalignment of the shaft, permanent distortion of sets, sheared 
bolts at the hanger connections, and some rockfall. The elevator shaft was 
located just beyond the limit of Zone k, where no damage was observed in the 
access tunnel. Damage to the shaft may be attributed to the different orienta- 
tion of the shaft with respect to the expanding shock wave as compared with the 



- 31 - 



l/\ 






£ £ 




3 




•— r— 




— fl> 




tO 3 




U- *J 




C — < 




O oj 




14- — O 




o »•- 




</> +J 




u) <U >• 


„ , 


+J s- — 


>» 


— Q. (D ,' 




EEC x 


c 


— on? /' 


— o 


_l O >- ' / /a 


Q. > 


^f 


5 
u- i 
O Q- 


1 


+j e 


1 


— o 




J 




in 

c 
o 
a. 
«/» 

<D 



C 

c 

3 



C 



E 



o 



-o 
o 

+J 

<u 

E 



O 

c 

Q> 

a) 

4- 
0) 

a: 



«j E 
o o 

— i_ 



Q. 

E 
<u 

«/) 

3 
(/) 

l_ 
0) 

> 



f0 

o 



c 

< 






o> 



+J 
< 



a- O 

4) +J 



- 32 - 



tunnel's orientation. In addition, the response of the shaft was probably 
affected by the looser deposits and more weathered rock near the ground 
surface. 

Damage to the 15 test sections in Drift C is detailed in Table 3- The severe 
damage of the unlined circular section (C2a) is consistent with a location 
well within Zone 3. The rock bolts and wire mesh of an adjacent circular 
section (C2b) reduced the damage somewhat by preventing large rocks from 
dropping. On the other hand, the square sections (C1a and CI b) that were 
unlined or were supported with rock bolts and wire mesh were completely 
closed. Heavier damage to square sections as compared with circular sections 
is to be expected because square sections are inherently the weaker of the two. 
Moreover, the square sections were excavated through a highly fractured zone, 
which probably contributed to their destruction. The horseshoe-shaped sections 
supported by steel sets and wood lagging experienced moderate to severe damage. 
The main mechanism of failure seems to have been the heaving of the floor, 
which dislodged the invert timber struts. This, in turn, permitted the bottom 
of the sets toward the zero point to be kicked inward. The rigid (concrete) 
liner without backpacking received moderate to light damage. The remaining 9 
sections, all with backpacking of some kind, were negligibly damaged. Little 
difference between the type of liner, the type of backpacking, and the thickness 
of the backpacking was noted, indicating that the important factor for these 
sections was the mere presence of the backpacking. 

All sections in Drift B were either closed or severely damaged, with one notable 
exception. A rigid liner with a thick backpacking had negligible damage. The 
similar section in Drift A remained open but suffered severe damage, while all 
other sections in Drift A were completely closed. 

Response Data . Response measurements in test sections are not particularly useful 
for this review: the few mechanical gages that were recovered were badly damaged 
and electronic gages provided only a limited amount of data about strains and 
particle velocities for liners in Drifts A and B. However, the free-field data 
obtained from stations along the access tunnel are useful. Experimentally deter- 
mined relationships were plotted for peak acceleration, particle velocity, strain, 
and stress parallel to the direction of the shock. Values of these quantities 

- 33 - 



Table 3- Summary of damage in Drift C, Shot Hard Hat. 



Section 
Njmber 


Cross Section 
Shape and Size 


Liner and 
Backpacking 


Geology 


Damage 


C2d 


circular 
8.00-ft diameter 


rock bolts and 
wire mesh 


granite -- 
competent, but 
degree not 
described 


severe to moderate damage, 
maximum breakage 1-1/2 ft 
thick, pieces 2 in. to 6 in. 
or larger, mesh torn loose 
from bolts at one place 


C2a 


circular 
8.00-ft diameter 


unlined 




severe to moderate damage, 
maximum breakage 2-1/2 ft 
thick 


C6c 


circular 
7.50-ft diameter 


8-gauge steel 
9-in. cinder back- 
packing 




negl igible damage 


C3a 


circular 
8.00-ft diameter 


12-in. reinforced 
concrete cast 
against rock 




moderate to light damage, 
liner crushed at one place 
exposing buckled reinforcing 
bars, maximum rock breakage 
1 ft 


C4c 


circular 
9.67-ft diameter 


steel set/wood lag- 
ging, 5-in. foam 
backpacking 




negligible damage 


C3d 


circular 
9.50-ft diameter 


12-in. reinforced 
concrete 

9-in. cinder back- 
packing 


n 




C6e 


circular 
10.00-ft diameter 


8-gauge steel 
20-in. foam back- 
packing 






C3c 


circular 
11.33-ft diameter 


8-in. reinforced 
concrete 

20-in. foam back- 
packing 






C3b 


circular 
9.50-ft diameter 


12-in. reinforced 
concrete 
5-in. foam back- 
packing 






C4a 


circular 
9.92-ft diameter 


steel set/steel lag- 
ging, 9-in. cinder 
backpacking 


■I 




C4fc 


circular 
9.92-ft diameter 


steel set/steel lag- 
ging, 5-in. foam 
backpacking 






C6b 


circular 

7.50-ft diameter 


8-gauge steel 
5-in. foam back- 
packing 


granite — 
not as compe- 
tent as in C3c 
through C4b 




C7a 


horseshoe 
8.67-ft width 
9.33-ft height 


steel set/wood 

lagging 

no backpacking 


granite -- 
blocky, close 
to fault zone 


severe to moderate damage, 
floor heaved 5 ft, struts 
dislodged, crown bearing 
plate bolts failed 


Cla 


square 
8.00-ft 


unlined 


granite -- 

intensely 

faulted 


completely closed 


Clb 


square 
8.00-ft 


rock bolts and 
wire mesh 


11 


assumed completely closed 



NOTE: 1 ft = 0.30^8 m; 1 in. = 2.5^ cm. 



- 3*t - 



for various ranges were determined from these plots and are shown in Table k. 
Values for peak particle velocity and strain at the limits of Zones 3 and k are 
of the same order of magnitude as the values obtained from the UET program. 
However, it should be noted that accelerations experienced in Zones 3 and 4 
greatly exceed accelerations for earthquakes by several orders of magnitude. 

Observations . Some important observations that may have implications for earth- 
quake motion can be drawn from the results of the Hard Hat tunnel tests: 

• Horseshoe-shaped steel sets were vulnerable at the 
invert where heaving of the floor dislodged invert 
timber struts. 

• The damage sustained in highly fractured rock was 
more severe than in the more competent rock. 

• Thick concrete liners cast against the rock did not 
perform as well as thick concrete liners with back- 
packing, indicating that backpacking protects the 
liner in a shock loading. 



SUMMARY AND CONCLUSIONS 

The literature regarding the effects on tunnels, mines, and other large under- 
ground structures from shaking caused by earthquakes and underground explosions 
has been reviewed. Specific conclusions can be drawn from the studies on earth- 
quake damage to tunnels in rock. Data from conventional mine blasting provide 
upper limits to the peak ground motion parameters that are associated with 
various kinds of tunnel damage. The colossal explosions of the UET program 
and the UNE tests create ground motions far more severe than those from earth- 
quakes; however, these extreme situations provide insight into the dynamic 
behavior of tunnels that may be useful in understanding earthquake performance 
of underground structures. 

The following conclusions represent the major findings of this review: 

1. Little damage occurred in rock tunnels due to 

earthquake shaking when accelerations at the ground 
surface were below 0.*tg. Studies found that there 
was no damage in lined or unlined tunnels for ground 
surface accelerations below 0.19g and that there were 
few cases of even minor damage, such as fall of loose 
rock and new cracks in concrete linings, for surface 



- 35 - 



Table 4. Approximate peak values of measured free-field 
quantities versus range, Shot Hard Hat. 



Point of 


Interest 


Slant 

Range 

(ft) 


Acceleration 

(g) 


Particle 

Veloci ty 

(fps) 


Strain 
( in. /in.) 


Stress 
(psi) 


Li mi t of 


Zone 1 


NA 


NA 


NA 


NA 


NA 


Drift A 




244 


6,000 


90 


.0022 


45,000 


Drift B 




334 


1,100 


40 


.0011 


19,000 


Point of 


Closure 


375 


700 


30 


.0010 


15,000 


Limi t of 


Zone 2 


425 


330 


20 


.0008 


11,000 


Drift C 




457 


260 


18 


.0007 


10,000 


Limit of 


Zone 3 


550 


100 


11 


.0004 


6,000 


Limit of 


Zone 4 


775 


20 


6 


.0002 


3,000 



NOTE: 1 ft = 0.3048 m; 1 fps = 0.3048 m/sec; 1,000 psi = 6.895 MPa. 



-36 - 



accelerations between 0.19g and O.^g. 17 ' 24 As previ- 
ously discussed, these values of acceleration must be 
regarded as approximate and tentative for the present 
time because of the limitations of the studies from 
which they were derived. 

2. Severe damage and collapse of rock tunnels from earth- 
quake shaking occurred only under extreme conditions, 
such as ground surface accelerations exceeding 0.5g, 
marginal construction, and poor rock. 17 ' 24 Furthermore, 
complete tunnel closure was not due to shaking alone but 
appeared to be associated with movement of an intersect- 
ing fault or other major ground movement. 

3. Damage to cut-and-cover structures may be primarily 
attributed to large increases in lateral earth pressure 
during seismic motion and to inadequate design for such 
seismic loads. 

k. The peak particle velocity threshold of 12 in. /sec 
(30 cm/sec) for minor damage to unl ined rock tunnels 
from conventional mine blasting correlates well with 
the threshold of 8 in. /sec (20 cm/sec) found for earth- 
quakes. 

5. The colossal underground explosion tests (UET and UNE) 
indicate that minor damage to unl ined rock tunnels, 
such as fall of rocks partially loosened by excavation 
and weathering, may be effectively prevented by thin 
concrete lining or by rock bolts and wire mesh. 

6. In the UNE tests, tunnels in highly fractured rock were 
more severely damaged than tunnels in more competent 
rock. A similar comparison of damage to tunnels in 
these types of media is to be expected from the much 
less severe ground motion of an earthquake. 

7. Okamoto found that thicker liners suffered more damage 
than thinner (and more flexible) liners. 33 The same 
findings were obtained from the UNE tests. 

8. The collapse of horseshoe-shaped steel sets during the 
UNE tests was partly due to the dislodgement of timber 
invert struts. This would indicate that, if they are 

to be functional during ground motion, the invert struts 
should be securely fastened to the base of the sets. 



- 37 - 



4. Seismic Analysis 



It is appropriate to review the theory and current approaches used in the 
analysis of underground seismic stresses before discussing the wave propagation 
study and the state-of-the-art review of current techniques in seismic design 
of underground structures that were conducted for this investigation. The first 
section of this chapter focuses on present techniques for estimating subsurface 
stresses and strains in the free field (that is, away from the underground 
structure). The discussion includes an assessment of current methods of deter- 
mining subsurface ground motion amplitudes by inverting surface observations 
and an evaluation and review of various methods used for calculating stresses 
and strains around underground structures. The second section discusses earth 
material properties that must be considered in the analytical procedures and 
reviews the methods for measuring or estimating the properties. 

CURRENT TECHNIQUES USED IN SEISMIC ANALYSIS 

Available Numerical Models 

Numerical techniques employed in geomechanics have been extensively presented 
in the literature and are adequately reviewed in several publ icat ions. 1 * 2 jtt3 
For this discussion of dynamic problems in geomechanics, the principal methods 
of analysis are briefly described. The three main approaches reported in the 
literature are: (1) the lumped-parameter method, (2) the finite-difference 
method, and (3) the finite- element method. In each of these approaches, the 
geological structure and the spatial variables are uniquely discretized. In 
lumped-parameter models, the masses are physically lumped and are connected by 
springs and dashpots. Discretization is achieved for finite-difference models 
by replacing the continuous derivatives with respect to the spatial variables 
by ratios of changes in the unknown variables over a small but finite spatial 
increment. Finite-element models are generated by dividing the body into an 
equivalent system of finite elements (or small continua), a process that dis- 
cretizes the mass and stiffness of the body. 

The system of equations governing motion for each of the three models can be 
solved directly in the time domain by one of a variety of methods available 

- 38 - 



for step-by-step integration. The solution of the equations of motion can also 
be obtained indirectly in the frequency domain and then transformed into the 
time domain by using the inverse Fourier transformation. A third solution pro- 
cedure is the use of modal analysis, a method that is used in the field of 
structural dynamics. Because a discussion of the working details and limitations 
of each of these solution techniques is beyond the scope of this report, the 
interested reader is referred to the literature on the subject.^ 2 ' 43 

Two other numerical formulations deserve attention. The method of character- 
istics is uniquely suited to solving the problem of wave propagation because 
the procedure simulates the physical process of propagation. The set of partial 
differential equations governing the propagation of waves in a medium is con- 
verted into a set of ordinary differential equations, in time only, using char- 
acteristic lines or paths of propagation. This method has proven to be very 
economical for certain applications; however, it can be difficult to use when 
the material is nonhomogeneous or nonlinear.^ 3 

Boundary integral methods form a class of numerical procedures that may have 
great potential for the solution of subsurface dynamic problems. There are 
currently three different formulations of these methods: the boundary element 
method, the displacement discontinuity method, and the boundary integral equa- 
tion method. The advantage of these methods over the finite-element and finite- 
difference methods is that only the boundaries of the underground cavity (and 
perhaps the ground surface) are represented by a finite number of segments. 
Otherwise, the region would extend to infinity in all directions, and there is 
no need to discretize a large region or to establish fictitious boundaries, as 
is the case in finite-element and finite-difference models. Most applications 
of the boundary integral methods have been to mining and other static load 
problems; so far, there have been very few applications to dynamic geotechnical 
problems. These methods are still under development; however, they show promise 
for the future. 

Analysis of Free-Field Stresses and Strains 

Simple Free-Field Analysis . The simplest analysis for seismic stresses within 
a soil or rock mass is derived from the principles of plane wave mechanics. 



39 - 



Two types of plane waves can propagate through an elastic, isotropic body of 
infinite extent: congressional (P) waves and shear (S) waves. (For more details, 
see Appendix D.) Assuming the propagation of a P-wave, the axial strain, e, is 
given by 1 * 1 * 

6 = "V V (1) 

P 

where v is the particle velocity, and V is the velocity of the P-wave in the 
medium. The axial strain and the particle velocity are both in the direction 
of the propagation. By this approach, the maximum axial strain at any given 
point is due to the peak particle velocity that occurs at that point: 



I peak I 

e 



(2) 



(3) 



max v 

P 

Assuming a linear elastic, isotropic material in plane strain, the normal 
stress is 

ff(1 - v) e 
(1 + v}(1 - 2v) e 

where E is the Young's modulus, and v is Poisson's ratio. Thus, the maximum 
normal stress is 

+ ffO - v) peak I /a 

max " ( 1 + v) ( 1 - 2v) V v ' 

Using the relation 



V = Ej±z_v) (5) 

p J p(1 + v)(1 - 2v) 

where p is the density of the material, we can rewrite Equation (4) as 

a = ±pV \v . I (6) 

max p l peak 1 

A similar expression can be determined for the shear stress due to the propa- 
gation of an S-wave. In this case, the maximum shear strain is 



40 - 



_ + I n>peakl . . 

Y max " V ^'' 

s 

where v is the particle velocity normal to the direction of propagation and 
V is the velocity of an S-wave in the medium. The maximum shear stress is 

IWakl 

max V v ' 

s 

where G is the shear modulus. 



Since 



then 



V = [?■ (9) 

s v P 



x = ±p7 b . I (10) 

max s 1 n,peak' 



The above approach is based upon an obviously oversimplified characterization 
of motion within the soil or rock mass. The material is assumed to be linear 
elastic and isotropic. Maximum stresses at a point are estimated assuming 
that the peak particle velocities are known or can be estimated at that point. 
The approach does not address the effects of multiple reflections within soil 
layers, free-surface reflections, nonlinear soil behavior, or time characteris- 
tics of the wave motion. The one virtue of this approach is that it offers a 
simple, albeit very approximate, method for calculating stresses below the 
surface of the ground. 

More Refined Free-Field Analysis . The analysis of seismic stresses in the free 
field (that is, in the ground away from a structure) should appropriately ac- 
count for the complexities in both the geologic medium and the wave form. De- 
tails on the form of the wave motion and the influence of geology on wave prop- 
agation are considered at length elsewhere in this report. It is sufficient for 
the discussion that follows to point out that the underground wave motion 
consists largely of body waves (compress ional and shear waves) and surface 
waves (Rayleigh and Love waves). It is not possible in the current state of 
the art of seismology to break down a given time history of seismic motion into 
components of body waves and surface waves, although it is possible to recognize 

- 41 - 



their signatures in the wave form. Thus, it is not currently possible to use 
a time history of motion recorded at some point in a soil or rock mass to 
determine with reasonable accuracy the motion at some other point- 
Theoretical approaches to determining underground seismic motion at some desired 
point on the basis of observations at another point are of necessity simplified 
in terms of both geology and the wave form. Conventionally, seismic motion is 
assumed to consist of a train of shear waves propagating vertically upward from 
bedrock. These models assume one or more layers of homogeneous soil over bed- 
rock, the latter often taken as a rigid base. These assumptions severely re- 
strict the representation of the real problem. The assumption of vertically 
propagating shear waves has its origin in the early development of seismic anal- 
ysis of surface structures. Because all surface structures are designed to re- 
sist gravity or vertical loads, it was rightly felt that the primary concern for 
seismic resistance should be lateral or horizontal loads. This view, in turn, 
led to characterization of only the horizontal components of ground motion as 
inputs to the surface structure. Moreover, as seismic motion radiates from the 
source, it is continually refracted by the layering of surface material so that 
the body waves arrive with a nearly vertical incidence to the ground surface and 
not in a straight line from the source to the site. If the body waves are propa- 
gating vertically to the surface, then the compressional waves would contribute 
only to the vertical motion. Because it was assumed that only the horizontal 
motions need be considered for seismic analysis of surface structures, it became 
conventional to assume that the motion of interest consists only of vertically 
propagating shear waves. Clearly, the conventional approach has severe limita- 
tions in representing the actual motion within the free field. More rigorous 
models that represent more of the complexities of the problem are only now 
being developed. 

In the conventional approach, the amplification characteristics of a horizon- 
tally stratified soil mass are established using the theory of propagation of 
plane waves. 43 As previously noted, plane waves in an infinite medium consist 
of compressional (P) and shear (S) waves. When these waves propagate through a 
horizontally layered soil mass, they are reflected by the free ground surface 
and refracted as well as reflected by the horizontal interfaces between the 
layers. In order to discuss this phenomenon, it is necessary to resolve the 

- hi - 



S-wave motion into two components: one in a horizontal plane and the other in 
a vertical plane (both components being normal to the direction of propagation 
of the S-wave). The horizontal shear component is referred to as the horizon- 
tally polarized shear wave (SH-wave) , and the vertical shear component as the 
vertically polarized shear wave (SV-wave) . (For additional description, see 
Appendix D.) 

Consider, first, horizontally polarized shear waves propagating through a horizon- 
tally stratified soil mass. A train of SH-waves traveling upward through such a 
medium will be reflected and refracted at the interfaces between the layers and 
finally reflected at the free surface, which will result in trains of SH-waves 
traveling both upward and downward. Figure 11 illustrates the reflection and 
refraction of SH-waves, assuming some arbitrary angle of incidence. Satisfying 
the continuity of displacements and equilibrium of shear stresses at each inter- 
face, an amplification function can be developed that gives the ratio of the 
amplitude of the surface motion to the amplitude of the bedrock motion as a 
function of frequency. An example of such an amplification function is illus- 
trated in Figure 12. For multiple strata over bedrock, the SH-wave is usually 
assumed to be propagating vertically. The explicit forms for amplification 
functions for multiple strata are quite involved and do not lend themselves to 
hand calculation; however, numerical computations can very easily be performed 
on a digital computer using a computer code such as SHAKE. 45 

P-waves and SV-waves propagating vertically can be easily handled in the same 
fashion because vertically propagating P and SV effects are uncoupled. The 
solution for the SV-waves is identical to that for the SH-waves, while the 
solution for the P-waves is identical in form to an appropriate change in the 
elastic modulus/" If either P- or SV-waves are not propagating vertically, 
both P- and SV-waves are created during reflections, which results in coupling 
between them. This situation is quite complicated and requires further analy- 
sis; 46 however, the conventional approach considers only vertically propa- 
gating waves. 



*G in the solution for the SH-wave is replaced by E{\ - v)/(1 + v) (1 - 2v) to 
obtain the solution for the P-wave. 



- A3 - 



Free Surface 




Bedrock 

Figure 11. Reflections and refractions of SH-waves in a 
horizontally stratified soil mass. 



05 



03 

o 



Q. 

E 
< 




Frequency (Kz) 

Figure 12. Typical example of the amplification function 
for a soil layer over bedrock. 



- kk - 



The amplification function of the soil can be used to determine a time history 
at the surface of the free soil. Given a specific accelerogram assumed to 
represent the earthquake motion at bedrock, the corresponding time history can 
be determined at the free surface of the soil by (1) obtaining the Fourier 
transform of the input time history at bedrock, (2) multiplying the Fourier 
transform time history by the amplification function of the soil, and (3) 
applying the inverse Fourier transform back to the time domain. This procedure, 
assumes that the recorded time history is the result of waves of a specific 
type, usually vertically propagating shear waves. Because this discussion 
omits the details and intricacies of the procedure, the interested reader may 
wish to refer to the literature on the subject. 43 

An earthquake time history can be constructed at the ground surface from a given 
time history at bedrock using the above procedure. In many situations, 
however, the inverse procedure is required. Often ground motions are specified 
at the soil surface (or very close to the soil surface), and the motion at some 
point within the soil column or at the bedrock is desired. This inverse, or 
deconvolution, process requires the application of the transfer function from 
the top of the soil column to the bottom, which is just the inverse of the 
transfer function from the bottom to the top. 

The lumped-parameter approach has been particularly popular among practicing 
engineers for the determination of one-dimensional amplification and deconvo- 
lution. The discrete model suggested by Seed and Idri ss 47 » 48 assumes verti- 
cally propagating waves and horizontal soil layers as illustrated in Figure 13* 
Most studies using this method assume linear elastic soils and, in some cases, 
viscoelastic soils. However, during strong shaking, the soil behaves non- 
linearly, and a linear model is not representative of actual behavior. The 
inclusion of nonlinear models in the deconvolution process greatly compli- 
cates the computational task for the lumped-parameter model. 

A method that accounts for the nonlinear effects in soils during strong earth- 
quakes was proposed by Seed and Idriss 47 through the introduction of the 
equivalent linear method. 49 Curves of the soil moduli and damping character- 
istics with respect to strain level are needed. first and are determined experi- 
mentally. The nonlinear behavior of the soil is simulated by an iterative 



- k5 - 



Layer 1 



P1<?1 



mi = 1/2pifci 
ki = Gi/hi 



Layer j 



Layer n 



% 'ft 



P G 
n n 



in n n 

:w — :»ro; 11 



Qm. = 1/2p.L + 1/2p, i. . 
J J J J- 1 J- 1 




fe . = G./h. 
J J J 



V,x,- 



V-T'C / 1 Bed rock''' ~- 'j V-f' 



h. = 

j 

G. = 
J 

P.- = 



height of layer j 

shear modulus of layer j 

density of layer j 



a. Layered 
soi 1 



mass 



b. Lumped-mass 
and spring 
model 



Figure 13. Lumped-mass and spring idealization of a 
semi-infinite layered soil mass. 



- 46 - 



procedure that assumes a linear soil response in each time step and matches the 
moduli to the level of strain from experimentally determined curves. Conver- 
gence cannot be guaranteed for this trial-and-error procedure, and problems 
often arise for deep or soft soil strata, particularly for strata containing 
very thin layers of soil with material properties that contrast highly with the 
adjacent soil layers. 

The finite-element approach is currently enjoying widespread use for the deter- 
mination of strains and stresses within a soil mass. The inclusion of nonlinear 
soil behavior usually does not pose any serious problem for the finite-element 
method. The most common approach is the equivalent linear method described above. 
One of the most widely used finite-element programs at this time is the FLUSH pro- 
gram, which assumes vertically propagating shear or compressional waves. 50 

Boundary conditions often pose problems in the finite-element method. The dis- 
cretization of a continuum by finite elements results in a finite domain with 
well-defined boundaries. If these boundaries do not correspond to the natural 
boundaries within the soil structure, then artificial reflections of wave 
energy will take place, leading to erroneous results. One method for over- 
coming this difficulty is to locate the boundaries sufficiently far away from 
the point of interest in the soil mass so that undesirable reflections will not 
arrive at that point during the time of observation. Such an approach can lead 
to extremely high computational cost. The second approach employs transmitting 
or viscous boundaries. For example, viscous dashpots, first suggested by 
Lysmer and Kuhlemeyer, 51 are used in the FLUSH code. 

Selected Computer Codes for Free-Field Analysis . To conclude this section on 
the analysis of free-field seismic motion, a few of the computer programs 
available for the computation of motion at depth are discussed: 

• The SHAKE 45 program computes the response in a horizon- 
tally layered soil and rock system subjected to tran- 
sient vertically propagating shear waves. The method 
does not rely upon a discretization scheme but rather 
uses transfer (amplification) functions. Nonlinear soil 
behavior during severe seismic motion is represented by 
the equivalent linear model described above. This pro- 
gram can determine subsurface ground motions by decon- 
volution from a surface record as well as surface 



- k7 - 



motions by direct computation with an input record at 
bedrock. 

The computer program MASH 52 has capabilities similar to 
those of SHAKE in that it is designed to solve the dy- 
namic response of a horizontally layered soil deposit 
to vertically propagating shear waves. However, with 
MASH the soil mass is discretized into a string of one- 
dimensional constant strain finite elements with masses 
lumped at the nodes. The characterization of the soil 
in the program MASH may be either viscoelastic or non- 
linear with rate- independent damping. 

Another computer program for calculating the one- 
dimensional behavior of soils is the code CHARSOIL, 53 
which employs the method of characteristics. Input 
motions may be introduced only at the rock-soil inter- 
face; therefore, CHARSOIL cannot handle the decon- 
volution problem. The response of the soil can be 
evaluated on the basis of elastic, viscoelastic, or 
nonlinear (Ramberg-Osgood) soil behavior. 

0JJAKE 51+ is a one-dimensional, explicit, finite- 
difference code for the propagation of shear waves 
through nonlinear soil layers. Its capabilities are 
very similar to those of SHAKE; however, instead of 
the equivalent linear soil model used in SHAKE, 
QUAKE is able to follow arbitrary stress-strain 
curves in very small time steps. 

Banister et al. 55 developed a program to study the 
stresses and strains due to reflection of seismic body 
waves (SH-, SV-, and P-waves) from the ground surface, 
the incident wave propagating with an arbitrary angle 
of incidence rather than propagating only vertically. 
However, this program was written for a homogeneous 
elastic half-space and is not applicable to a layered 
soil site. Furthermore, the program was not written 
to consider the deconvolut ion problem. 

Nair and Emery 56 included the propagation of both 
surface and inclined shear waves in a linear, homo- 
geneous, horizontally stratified soil structure. Their 
program does not consider the deconvolut ion problem. 

The FLUSH 50 program, developed for the analysis of the 
interaction of surface structures with the soil mass, 
solves both the direct computational and deconvolu- 
tion problems, assuming vertically propagating shear 
or compress ional waves. FLUSH is a finite-element pro- 
gram that makes use of transmitting and viscous bound- 
aries. Nonlinear soil behavior can be approximated by 
the equivalent linear model. This code was developed 
for near-surface applications of soil-structure inter- 
action; therefore, it is not appropriate to use the 
FLUSH code for the determination of motion at great 
depths. 



- 48 - 



• STEALTH 2D is a finite-difference program specifically 
written to solve two-dimensional elastic wave propaga- 
tion problems. 57 The parent program, STEALTH, 58 was 
written to solve nonlinear, large-deformation transient 
problems, and it is assumed that STEALTH 2D will even- 
tually incorporate the same nonlinear features. STEALTH 
2D has been used to study the direct computation of 
wave motion in a soil mass due to both vertically and 
obliquely propagating SH-waves. 

Seismic Analysis of Underground Structures 

The following discussion focuses primarily on linear structures, such as tunnels 
of all kinds. Underground chambers and reservoirs will be discussed briefly. 
The response of tunnels (lined or unlined) to seismic motion may be understood 
in terms of three principal types of deformation: axial, curvature, and hoop. 
Axial and curvature deformations develop when waves propagate either parallel 
or obliquely to a tunnel. Axial deformations are represented by alternating 
regions of compressive and tensile strain that travel as a wave train along 
the axis, as shown in Figure 14. Curvature deformations create alternate 
regions of negative and positive curvature propagating along the tunnel, as 
shown in Figure 15- A tunnel liner that is very stiff compared with the sur- 
rounding soil responds as an elastic beam. For positive curvature, the liner 
will be in compression on the top and in tension on the bottom. This situation 
is correctly assumed in the literature on seismic design of subaqueous tubes 
and subway tunnels. 59 ' 50 For the rock tunnel with a flexible lining or with 
no lining at all, the tunnel in positive curvature experiences tensile strains 
on the top and compressive strains on the bottom. 

Hoop deformations result when waves propagate normal or nearly normal to the 
tunnel axis. Two effects of these deformations might be observed. One is a 
distortion of the cross-sectional shape that creates stress concentrations in 
the hoop stresses, as shown in Figure 16. The other effect is that of ringing -■ 
the entrapment and circulation of seismic wave energy around the tunnel — 
which is possible only when wavelengths are less than the tunnel's radius. 5 - 1 

The simplest approach to analyzing stresses around underground structures is 
to use the simple expressions for free-field stresses that were previously pre- 
sented as Equations (6) and (10): 



- k3 - 



Tension Compression 






CUHl^ 



W^-;v 



'.JL^- 



I A^> 



Tunnel 









Figure 14. Axial deformation along tunnel. 



■'-it 



Posi ti ve 
Curvature 




Negative 
Curvature 



Figure 15- Curvature deformation along tunnel 



Tunnel during 
Wave Motion 




Tunnel Cross Section 
before Wave Motion 



Figure 16. Hoop deformation of cross section, 



- 50 - 



o = ±pV \v . 

max p 1 peak 1 

t = ±pV \v . I 

max s' n,peak' 

These expressions do not account for the presence of the structure and can 
be useful only in a qualitative evaluation of the stability of an opening in 
rock. This simple approach was taken in the evaluations of a cavern for an 
underground powerhouse 62 and of tunnels for a nuclear waste repository. 63 

Hoop Deformations by Classical Methods (Circular Sections Only) . The con- 
centration in the circumferential stresses due to hoop deformation may be 
estimated from simple expressions for free-field stresses as outlined by 
Chen et al. 6tf Mow and Pao 65 have studied the interaction of steady-state 
waves with cylindrical cavities in cases where the propagation direction is 
normal to the longitudinal axis, as illustrated in Figure 17- 

Consider first the stress concentration for the P-wave. The analogous static 
solution is Kirsch's solution for biaxial loading. When a static compressive 
stress of value a is applied in one direction and the lateral directions are 
constrained, the lateral compressive stress is a v/( 1 - v) , as illustrated in 
Figure 18. The stress concentration factor for this static loading, which 
occurs at the cavity wall for \p = tt/2, is given by 

Zi = 3.0 - — 5L_ (11) 

a Q 1 - v 

The dynamic stress concentration for a P-wave was determined by Mow and Pao 
for an isotropic, elastic medium and found to depend upon Poisson's ratio 
(as does the static analogy) and the dimensionless frequency of the wave, tt, 
as shown in Figure 19. The dimensionless frequency is defined by 

Q = f- (12) 

P 

where w is the circular frequency of the wave and a is the radius of the 
circular cavity. Note that SI = corresponds to an infinitely long wavelength, 
which is the static solution given by Equation (11). The peaks in dynamic 
stress concentrations are approximately 10% to 15% greater than the static 



- 51 - 



Simple Harmonic 
P-Wave, 



SV-Wave, 

or 

SH-Wave 



y 



Infinitesimal Element 
at Cavity Wal 1 





Figure 17- Circular cylindrical cavity and incident wave. 



1 


Jf V V \ 


r 




^ 
















i 


, i ,, ,, , 


i 



V 



Figure 18. Biaxial stress field created by a horizontal pressure. 



- 52 - 




1 2 3 

Dimensionless Frequency, ft 



Reprinted by permission of the publisher. 



Figure 19. Dynamic stress concentration factors for P-wave. 
(Adapted from Reference 65.) 



- 53 



stress concentration values and occur at Q - 0.25, or at wavelengths approxi- 
mately equal to 25 times the cavity radius. By selecting the largest value 
of the stress concentration factor over the entire range of frequencies for a 
given value of Poisson's ratio, Mow and Pao constructed a plot of the dynamic 
stress concentration versus Poisson's ratio for P-waves (Figure 20). 

The dynamic stress concentration for an in-plane SV-wave was also determined 
by Mow and Pao. Because the propagation direction is normal to the longi- 
tudinal axis of the cylindrical cavity, which is oriented horizontally, the 
particle motion of the SV-wave is in the plane of the cross section. The equiv- 
alent static stress concentration factor is equal to k, regardless of the value 
of Poisson's ratio. The dynamic value, however, depends on Poisson's ratio, as 
well as on frequency. Again, by selecting the largest value over the entire 
range of frequencies for a given value of Poisson's ratio, a plot of the dynamic 
stress concentration versus Poisson's ratio for SV-waves was obtained (Figure 21), 

Mow and Pao 65 also studied the interaction of a steady-state SH-wave with a 
cylindrical cavity, in which the particle motion is normal to the plane of the 
cross section. The equivalent static stress concentration factor is equal to 2 
regardless of the value of Poisson's ratio. The dynamic value does not depend 
upon Poisson's ratio either, although it does vary with frequency. The maximum 
dynamic stress concentration is about 2.1 (5% larger than static) and corresponds 
to a value of ua/V equal to approximately O.h. 

o 

Peak stresses around a circular cavity can be estimated by using the dynamic 
stress concentration factors and the simple formulas for free-field stresses 
given by Equations (6) and (10) 



a 
max 



= ±K,qV \v . I 
1 p 1 peak' 



(13) 



T 



= ±KoV \v . I (1*0 



where 



max ~ 2 s 1 n,peak 



K, = the dynamic stress concentration factor for 
a P-wave (Figure 20) 

K 2 = the dynamic stress concentration factor for 
an SV-wave (Figure 21) 



- 54 - 



4.0- 



Reprinted by permission of the publisher. 



3.0 ___ 



*l 



2.0- 



Dynamic 




Static Equivalent, 
Equation (11) 



— I - 
0.1 



— I - 
0.2 



- r~ 
0.3 



— i— 
0.4 



Poisson's Ratio, v 



Figure 20. Maximum dynamic stress concentration factor 
Zj for P-wave incident upon a cylindrical cavity. 
(Adapted from Reference 65.) 



5.0 



Reprinted by permission of the publisher. 



K r 



4.0- 



3.0- 



Dynamic 



Static Equivalent 



~i 1 r~ 

0.1 0.2 0.3 
Poisson's Ratio, v 



0.4 



Figure 21. Maximum dynamic stress concentration factor 
K2 for SV-wave incident upon a cylindrical cavity. 
(Adapted from Reference 65.) 



55 



\v , I = the absolute maximum value of the particle 
velocity in the direction of propagation 

\v . I = the absolute maximum value of the particle 

velocity normal to the direction of propa- 
gation 

In practice it may be impossible to determine v , and v , separately, 

p6dK %yp£3K 

in which case the maximum particle velocity expected at the site, regardless of 
orientation, should be used. 

This simple approach to estimating peak dynamic stresses around an unlined 
cylindrical cavity can be extended to lined cavities; however, the mathematics 
is considerably more involved. Mow and Pao 65 investigated the case of a P- 
wave incident upon an elastic liner of arbitrary thickness embedded in an 
elastic medium (see Figure 22). The solution depends upon ratios of the shear 
moduli, the P-wave velocities, and the Poisson's ratio of the two materials, 
as well as on the ratio of the outer and inner radii of the liner. Mow and 
Pao plot values for the maximum dynamic stress concentration factor for the 
medium, K , and for the liner, K 1 , shown in Figures 23 and 2k, respectively. 

777 Is 

Poisson's ratios for both the medium and the liner are set to 0.25, while dimen- 
sionless parameters are defined by 

P = G -P- (15) 

G l 

a = pm (16) 

pi 

r = b/a (17) 

Note that the stress concentration in the medium is less than that in an unlined 
cavity and can be further reduced by using a thicker liner (larger value of r) 
or a stiffer liner material (larger value of G-). The stress concentration in 
the liner for a given r will, conversely, increase with increasing liner modulus. 

Note also that if the liner modulus is greater than the medium modulus (y < 1.0), 
Figure 2k predicts that a thin liner will increase the stress concentration in 
the liner. This does not imply that a thicker (hence a stiffer) liner is pref- 
erable in soft ground, however. The desirability of a flexible liner has been 
established for soft-ground tunnels under static loads. 1 Peck et al. 1 show that 

- 56 - 



Simple Harmonic 
P-Wave 




Factor 



^vj, Medium 

■ r i wz m pm 



stress 
Dv r>aW lC * 



-Concentva^ ^ 




..- -.->'/: 



G-j ,\)-, ,V 7 



Figure 22. Circular cylindrical liner and incident wave, 



57 - 



Reprinted by permission of the publisher 



2.0- 



K 



m 



1.0- 




Unl ined Cavity 



Figure 23. Maximum medium dynamic stress concentration factor K 



m 



versus liner thickness parameter r for various y and 

a (v = v- = 0.25). (Adapted from Reference 65.) 

ml 



Reprinted by permission of the publisher. 



K. 




1 
1.0 1.1 1.2 

Figure 2k. Maximum liner dynamic stress concentration factor in- 
versus liner thickness parameter r for various y and 
a (v = v 7 = 0.25). (Adapted from Reference 65.) 

Til Is 



- 58 - 



flexural moments in a liner decrease as the thickness of the liner is reduced. 
However, the maximum stress may increase because stress varies not only with the 
moment but also with the inverse of the thickness squared. Therefore, caution 
should be exercised when applying these curves. 

Although Mow and Pao consider only the P-wave incident on an elastic liner, Mente 
and French 66 present similar results for an SV-wave incident on an elastic liner. 

The procedures based upon Mow and Pao assume that no slip occurs between the 
liner and the medium. Slip at this interface is probably not likely during an 
earthquake, except possibly for tunnels in soft soils. Slip is a possibility 
under large dynamic loads, such as those created by a nuclear explosion, and 
it has received attention in literature on protective structures for defense 
applications. Solutions for springline thrusts and moments in liners have been 
obtained by Lew, 67 » 68 assuming full slip. The solutions are based upon small- 
displacement theory, which assumes that liner deflection from transverse shear 
stresses (perpendicular to the midsurface of the liner) are, negl igible. Lew's 
solution does not consider dynamic loading; instead, the equivalent static 
pressure is used with the assumption that the dynamic solution will be only 
10% to 15% greater than the static solution. 

Hoop Deformation by Computer Methods . Discrete models, such as finite- 
element and finite-difference models, provide excellent procedures for ana- 
lyzing dynamic hoop deformations of a cavity. These modeling procedures 
permit consideration of a variety of practical aspects: lined as well as 
unlined cavities, arbitrary cross-sectional shape, rock joints, nonhomogeneous 
material properties, and rock bolts, among others. The models can be used to 
investigate the response of a structure in close proximity to the free ground 
surface. 

Several computer programs are available for two-dimensional analysis of under- 
ground structures. SAP IV, 69 a finite-element structural analysis program, 
can be used to analyze linear systems. NONSAP 70 is a finite-element structural 
analysis program that permits consideration of geometric nonl inear i t ies and 
several different material nonl inear it ies for two-dimensional plane stress and 
plane strain elements. Unfortunately, NONSAP is not able to directly accept 

- 59 - 



acceleration time-history "pputs; the forcing function must be prescribed as 
a load history at any particular node. ANSYS 71 is another general -purpose 
analysis program that has capabilities similar to those of NONSAP when applied 
to two-dimensional plane problems. Significantly, these general-purpose struc- 
tural analysis programs do not contain nonref lect ing boundaries. Thus, unwanted 
waves may reflect from the boundaries of the finite-element mesh back to the 
underground structure during the observation time. The FLUSH 50 program does 
contain nonref lect ing boundaries and could be used to investigate near-surface 
openings for vertically propagating shear or compression waves. However, 
FLUSH was intended for analyzing the interaction between surface structures and 
the soil mass, and its use to model any other situation (such as underground 
structures) is not advised. Its use for deep structures would be both costly 
and inappropriate. Finite-difference codes such as STEALTH 58 are also availa- 
ble for modeling the dynamic response of two-dimensional underground structures. 
A nonref lect ing boundary has been formulated for a finite-difference code by 
Cundall et a1. 7 2 

Finite-element codes have been applied to the dynamic analysis of underground 
structures. A few are cited here for perspective. John A. Blume S Associates, 
Engineers, investigated the seismic stability of a railroad tunnel through Fran- 
ciscan Shale, a relatively weak and highly fractured rock. 73 The vertical cover 
above the tunnel varied in thickness from 23 to 37 ft (7 to 11.3 m) . The finite- 
element model was subjected to an acceleration time history from the Golden Gate 
Park (San Francisco) earthquake of 1957- Yamahara et al. studied the earth- 
quake safety of a rock cavern at a depth of approximately 250 ft (76.2 m) . 
The investigators used two acceleration time histories, one from the 1 9^+0 El 
Centro earthquake and the other from the 1968 Hachinohe earthquake. Glass 
determined stress concentrations around unl ined rectangular cavities using a 
finite-element model subject to triangular stress pulses. 6 Murtha employed 
a nonlinear finite-element code to study the dynamic response of a horizon- 
tally buried cylinder to very high shock loadings, such as those that might 
occur from the explosion of a nuclear weapon at the ground surface. 75 Wahi 
et al. investigated the stability of rectangular openings with the finite- 
difference code STEALTH using several different material models and several 
different earthquake time histories. 76 This investigation seems to be the 
first reported wave propagation study of an underground opening with two-compo- 
nent motion, one component being P-wave motion and the other SV-wave motion. 

- 60 - 



Large underground tanks (for the storage of liquefied natural gas, petroleum, 
or liquid nuclear wastes) also have been analyzed for seismic stresses using 
finite-element codes. 77 > 78 Such tanks are steel or concrete cylinders with 
their axes of symmetry in a vertical position They are usually buried at a 
shallow depth and are constructed by cut-and-cover operations. 

Developments are still under way on means to include many important rock mass 
properties, such as joint behavior, strain softening, dilatancy, tensile 
cracking, and plasticity, in the application of discrete models to static 
problems. The inclusion of such properties continues to be the subject of 
much discussion. For example, rock discontinuities in finite-element models 
for static analysis were discussed by Goodman et al , 79 and by Roberds and 
Einstein. 80 Slip joints have been included in the finite-element code BMINES, 
a three-dimensional computer code developed to analyze mining problems. 81 * 82 

In dynamic analysis, similar developments are under way. For example, the study 
performed by Wahi et al. employed an isotropic plastic model, a joint-slip 
model, and a tensile-cracking model. 78 The isotropic plastic model used the 
von Mises yield criterion and the Prantl-Reuss nonassociated flow rule. The 
joint-slip model simulated slip along the joints and accounted for dilation 
effects. The tensile-cracking model allowed new cracks to open up parallel to 
predefined joint sets and monitored the opening and closing of these cracks. 

An interesting approach, currently under development, to analyzing the response 
of caverns in rock is the discrete-element method (DEM), first devised by 
Cundal 1 .' 81+ The original method assumed that deformations occur only at 
element boundaries and that the elements themselves are rigid. That assump- 
tion corresponds to low-stress rock situations -- those in which displacement 
of joints far exceeds displacement of the intact rock blocks. Maini et al . 
undertook some major revisions of Cundal l's original work, among them: 

• Translating the original code written in machine lan- 
guage into standard FORTRAN 

• Developing a method for allowing blocks to crack and 
break into separate elements 

• Permitting fully deformable blocks 

• Proposing constitutive laws for rock joints 

- 61 - 



Dowding and Belytschko of Northwestern University are currently engaged in a 
project to develop a computer code, based upon Cundall's DEM, that will be able 
to account both for rock mass inhomogenei ties in the form of continuous joints 
or shear zones and for irregular geometry of the opening and the intact rock 
blocks. 86 

Boundary integral methods, introduced briefly in the beginning of this 
chapter, may provide very powerful numerical approaches in the future for 
the dynamic analysis of underground structures. The boundary element 
method (BEM) , one formulation of the boundary integral method, has already 
been applied to the analysis of static stresses around underground 
openings. 87 * 88 ' 89 We are not aware of applications of BEM to dynamic analysis 
of underground structures as yet. The boundary integral equation method (B I EM) 
has also been applied to static geomechanics problems, including the three- 
dimensional stress analysis of tunnel intersections. 90 ' 91 BIEM has been used 
for the dynamic analysis of soil-structure interaction of large rigid struc- 
tures on, or embedded in, the ground surface. 92 Alarcon et al. believe that 
the dynamic analysis of a lined tunnel can be easily treated with BIEM. 92 

Physical models may also be employed in the analysis of underground openings 
for ground motion. Barton and Hansteen 93 studied the dynamic stability of 
large underground openings at shallow depth using jointed physical models at 
a scale of 1:300. The model material consisted of a mixture of red lead, sand, 
ballotini, plaster, and water. Joint sets were produced in cured slabs of the 
model material by a double-bladed guillotinelike device. Displacements of the 
simulated rock blocks in the model were measured by means of photogrammetry. 
Another experimental procedure that might be used is dynamic photoelast ici ty. 
Daniel 94 has used such a technique to study the effects on underground struc- 
tures of blast waves moving over the ground surface. 

Axial and Curvature Deformations . Having discussed the various methods for 
analyzing seismic stresses around a tunnel due to hoop deformation, we now 
direct our attention toward the analysis for axial and curvature deformations. 
Axial or curvature deformation created by the passage of seismic waves results 
in cycles of alternating compressive and tensile stresses in the tunnel wall. 
These dynamic stresses are superimposed upon the existing static state of stress 

- 62 - 



in the rock and in the tunnel liner (if a liner is present). There are several 
failure modes that might result. Compressive seismic stresses add to the com- 
pressive static stresses and may cause spalling along the tunnel perimeter due 
to local buckling. Tensile seismic stresses subtract from the compressive static 
stresses, and the resulting stresses may be tensile. This implies that rock 
seams or joints will open, permitting a momentary loosening of rock blocks and 
a potential fall of rock from the tunnel roof and walls. 

The response of the medium and liner for axial and curvature deformation is 
most appropriately represented by a three-dimensional model. However, a 
one-dimensional model can be used for submerged transportation tubes, subway 
tunnels in soils, and steel or concrete pipes. Such structures can be treated 
as beams, permitting the application of standard structural analysis concepts. 
The only issues are the form of the ground motion input to the structure and 
the amount of interaction between the soil and the structure. Kuesel devised 
a deformation response spectrum method that prescribes a design curvature for 
the beam analysis. 59 Kuesel 's method, which was a first attempt at dealing 
with this problem, was later expanded by Kuri bayashi . 60 The revised method, 
referred to as seismic deformation analysis, utilizes a velocity response spec- 
trum for base rock, evaluated from observed strong-motion accelerations. It 
provides a very simple analytical tool for the determination of axial force, 
shear force, and bending moment on a tunnel section. The method has very 
practical applications for design and, therefore, is described in detail in 
the chapter on current practice in design (Chapter 6). 

A more refined model of the submerged tunnel has been proposed by Okamoto and 
fellow researchers. 33 ' 95 ' 96 For this model, the subaqueous tunnel is assumed 
to be an elastic beam that can deform axial ly and in bending. It is further 
assumed that the natural period of the soil is not influenced by the exis- 
tence of the tunnel and that the ground motions are only shearing vibrations. 
The soil layer above bedrock (or an appropriately stiff sublayer) is lumped 
into masses at discrete points along the tunnel. The mass points are connected 
in the longitudinal direction of the tunnel by springs that represent the 
relative axial stiffness and shearing stiffness of the layer between adjacent 
mass points. The soil masses are connected to the base by springs that 



- 63 - 



represent the shearing stiffness of the soil layer and are determined from 
the natural period of the soil and the lumped masses. 

Three-dimensional models are needed to analyze rock tunnels and caverns for 
axial or curvature deformation. Free-field stresses estimated by Equations (6) 
and (10) have been used to make a qualitative evaluation of stability in several 
studies. 62 ' 63 However, more realistic models would include the tunnel or cavern 
itself. If the cavity is a circular cylinder, then two-dimensional axisymmetric 
models could be used to study axial deformations, but not curvature deformations. 
Regardless of the geometric shape of the cross section, the curvature deforma- 
tions of a rock tunnel should be analyzed by a three-dimensional model. Computer 
codes such as SAP IV, NONSAP, and ANSYS currently provide the basic tools for 
such analyses. Unfortunately, the computer costs associated with three- 
dimensional models prevent studying anything more than the simplest configura- 
tions and input motions (or loads). 

PROPERTIES REQUIRED FOR SEISMIC ANALYSES 

The properties of soil and rock currently required for seismic analysis include: 

• density (p) 

• seismic wave velocities {V and V ) 

p s 

• dynamic moduli (E and G) 

• Poisson's ratio (v) 

• elastic damping (Q) 

Advanced methods of analysis that are still in the process of development 
will eventually be capable of incorporating joint and fracture properties and 
ani sotropy. 

Techniques for Measuring Soil and Rock Properties 

Density . Density, p, is readily measured on soil samples or rock cores in 
the laboratory. Errors in measurement can be reduced by careful use of undis- 
turbed sampling techniques, such as a Pitcher tube sampling of soils and triple 
tube core barrel sampling of rocks. 



- 6k - 



Characterization of the earth or the rock mass at a site remains a problem 
whose solution requires judgment and care because of the natural inhomogenei ty 
of these materials. Density, like all other material properties, is statisti- 
cally distributed, and the sampling technique employed may not lead to a true 
representation of the mean value even though the accuracy appears to be high. 
For example, even the most careful coring techniques will tend to underrepre- 
sent soft layers or shear zones within hard rock. This difficulty can be over- 
come by the use of a nuclear density probe that can take continuous measure- 
ments as it is lowered down a borehole. This is a standard approach in the 
petroleum industry. Because of high costs, borehole logging probes are cost 
effective only for critical facilities or in deep boreholes. 

Seismic Wave Velocities. Seismic wave velocities, V and V , are conventionally 

p s r 

measured in situ using geophysical techniques. A well-planned site investigation 
will employ a variety of these techniques in order to obtain a good three-dimen- 
sional characterization of the site. In situ geophysical techniques provide 
more realistic values than do laboratory methods because properties are measured 
across a large volume of the subsurface and include the effects of fractures and 
inhomogenei ties. However, seismic wave travel paths must be assumed, which can 
lead to inaccuracies for highly anisotropic and inhomogeneous site materials. 
A current description of seismic site investigation techniques is given by 
Wilson et al. 97 

Surface refraction is the most commonly used method. The travel time is mea- 
sured between the source of excitation, either an impact or an explosive charge, 
and a pattern of geophones spread across the ground surface. This method is 
used to measure nearly horizontally propagating compressional wave and shear 
wave travel times. However, relatively thin, soft layers are masked out wher- 
ever they are overlain by harder materials. 

Crosshole seismic techniques also yield velocities of horizontally propagat- 
ing waves. The seismic source is placed in one borehole, and the receivers 
are placed at the same depth in other boreholes. A depth profile may be made 
by lowering the entire array and repeating measurements at intervals. Dif- 
ficulties arise in knowing, with sufficient precision, the distance between 
points in two closely spaced boreholes. Crosshole seismic techniques afford 
better resolution of low-velocity layers than do refraction techniques. 

- 65 - 



Uphole and downhole techniques measure velocities of seismic waves propagating 
in nearly vertical directions. Uphole measurements are made with seismic 
sources in the borehole and the geophone array spread across the ground, 
whereas downhole measurements are made with the geophones in the borehole and 
the seismic sources on the ground. These techniques are favored for earthquake 
engineering because they employ vertically propagating waves, which are thought 
to account for most of the damaging seismic energy input to a surface site. In 
addition, these techniques, especially the downhole technique, are best for 
distinguishing low-velocity layers overlain by high-velocity layers. 

Velocity profiles can also be obtained by downhole probes that measure the 
travel time of impulses through the borehole wall from a transmitting source 
to a receiver. This technique has the advantage of continuous logging ability; 
but the effects of the casing, borehole wall, and short travel path make the 
results more useful for correlation of layers than for der i vat ion of site 
properties. According to unpublished data gathered by URS/John A. Blume & As- 
sociates, Engineers (URS/Blume), borehole logging has yielded velocities some 
20% to 25% higher than those obtained by downhole seismic surveys at the same 
locations. The work of Kanamori and Anderson 98 suggests at least a partial ex- 
planation; seismic velocities may be frequency dependent, with high-frequency 
signals traveling faster than low-frequency ones. 

Compressional and shear impulse velocities are commonly obtained in the labora- 
tory on intact specimens. Travel time of impulses is measured from one end 
of the sample to the other. Because this type of test involves short travel 
paths and small samples of the intact material, the results tend to under- 
represent joints and fractures. Therefore, seismic velocities obtained by 
this method may be biased toward higher velocities and should always be com- 
pared with field measurements. 

Dynamic Mpdul i . Dynamic values of the Young's modulus, E, and the shear 
modulus, G, are most commonly calculated from seismic wave velocities using 
the well-known formulas: 

E . = oV 2 0+ All - 2v) (l8 ) 

se,s P (1 - v) 

G . = pV 2 (19) 

seis w s 

- 66 - 



The uncertainties in E . and G . arise primarily from uncertainties in 

seis seis 

the seismic velocities used. Dynamic moduli are also obtained in the labora- 
tory on soil or rock specimens by two main methods: dynamic triaxial com- 
pression tests and resonant column tests, the results of which are E. „ . 
r dynamic 

and G, . , respectively, 

dynamic 

A typical dynamic triaxial compression test involves jacketing the specimen 

with a rubber sleeve and placing it in a pressure cell. A confining pressure 

is introduced to approximate the stress conditions at depth, and a consolidation 

piston load is applied. The piston load is then cycled; for cohesionless 

soils and rock, difficulties are encountered unless the piston load remains 

compressive to prevent tensile failure of the specimen. The modulus E. 

v v r dynamic 

is the slope of the axial stress-strain curve after a specified number of 

cycles. E, .will tend to decrease with repeated cycl ing and with in- 

7 dynamic r 7 3 

creasing strain level. Cycling frequencies on the order of 1 to 10 Hz are 
commonly used, depending on the stiffness of the specimen and on machine 
capabilities. Cyclic triaxial testing has become a standard test for deter- 
mining the dynamic properties of soils. "> (For example, it has been used in 
the assessment of liquefaction potential of sands.) Cyclic triaxial testing 
of rock, however, has only recently received attention. Haimson suggests 
standards for dynamic triaxial rock testing and describes methods of over- 
coming the special problems of testing rock materials that have high compres- 
sional strength, low tensional strength, and brittle behavior. 101 

The test cell configuration for resonant column testing is similar to that for 
triaxial tests; however, the dynamic load applied to the piston is torsional. 
Various frequencies are applied until a resonance is found at which sig- 
nificant strains are achieved. The modulus thus calculated is a torsional 

shear modulus {G, . ). Specifications for testing and methods of data 

dynamic r 3 

reduction are described by Drnevich, Hardin, and Shippy. 102 

Hendron published correlations between dynamic moduli determined for rock 
masses by in situ seismic tests and static deformation moduli determined by 
laboratory compression tests and by jacking and pressure chamber tests in 
dam abutments. 103 These correlations also include a rock quality designation, 
a measure of fracture frequency, as a parameter. Silver et al. showed that 

- 67 - 



for clay shales good correlations could be found between static moduli deter- 
mined with borehole pressure meters and dynamic moduli obtained from labora- 
tory cyclic triaxial tests. 104 Empirical correlations such as these indicate 
that, at least for certain foundation materials and selected sites, static 
tests conventionally used for design purposes may also provide a means of 
estimating dynamic properties, given sufficient site-specific data. 

Po is son's Ratio . Poisson's ratio, v, for dynamic analysis is typically cal- 
culated from field geophysical measurements of seismic velocities using a 
variation of the following relation, which is correct for an elastic medium: 

' w 2 - 2 

v " *-<yv«-. <20) 

It is apparent that Poisson's ratio is sensitive to uncertainties in the values 
of either of the elastic wave velocities. Field experience confirms this con- 
tention; therefore, Poisson's ratio must be assessed within the context of other 
exploration data and experience. 

Laboratory measurements of Poisson's ratio are accomplished by monitoring the 
lateral strain of a sample subjected to triaxial compression. However, the 
results of such tests do not represent the behavior (including discontinuities) 
of the site materials, nor do the boundary conditions placed on the test sample 
correctly model subsurface confinement. 

Damping . Although site damping, Q, is a property of great importance in soil- 
structure interaction calculations, developments in engineering geophysics have 
not kept pace with computational approaches to solving earthquake response 
problems. 

Site damping factors are typically specified on the basis of results of dynamic 
laboratory tests, such as those described above. Seed and Idriss showed that 
damping increases with strain amplitude in laboratory tests, and they derived 
empirical curves for estimation of damping for soils." 

In situ measurements of damping have not yet become commonplace; however, a 
limited body of experimental data indicates that site damping, at least in the 

- 68 - 



case of rock sites, is significantly greater than the damping found from 
laboratory tests. Damping (or attenuation) has been measured for near-surface 
geologic formations using explosives 205 ' 106 and on a crustal scale using spec- 
tral ratios of blast signals received at various distances. 107 These investi- 
gations have been primarily directed toward petroleum exploration and crustal 
seismology; virtually no applied work has been done in this area for earthquake 
engineering purposes. 

A simple methodology for derivation of in situ material damping factors is 
needed. Such a methodology is currently being investigated at URS/Blume by 
Bruce B. Redpath under a research grant from the National Science Foundation 
(Grant No. PFR-7900192) . Practical field techniques are being developed using 
downhole and crosshole surveys of seismic velocities and attenuation rates in 
holes 200 ft (61 m) deep at two different sites. The observed attenuation char- 
acteristics, corrected for geometrical spreading and changes of acoustic im- 
pedance in the ray paths, are being used to determine values of Q for the near- 
surface materials. Two methods of data analysis are be ing ( appl ied to impulsive 
signal sources: one determines Q indirectly by calculating the spectral ratios 
of both compress ional and shear pulses to determine the magnitude and frequency 
dependence of the attenuation coefficient in the exponential term of the propaga- 
tion equation; the other method tests a relationship in which the rise time of a 
seismic pulse is proportional to its travel time and in which the constant of 
proportionality is Q . A third approach to measuring Q uses an electronically 
controlled hydraulic vibration generator to generate monof requency signals over 
a range of 10 to 300 Hz; the attenuation of these signals with distance should 
provide values of Q without requiring the spectral analysis of complex pulses. 
The research will result in practical recommendations for field procedures and 
data analysis to measure ^-values in near-surface materials. 

Joint and Fracture Properties . It has long been recognized that the discon- 
tinuities in jointed or fractured rock can increase the deformabi 1 i ty and 
decrease the strength of the rock mass as a whole. Finite-element programs 
that include separate elements for intact rock and deformable joints have 
been developed and are undergoing improvements to make use of static properties 
such as joint friction, joint normal stiffness, and shear stiffness. These 
properties can be derived by jacking tests on rock blocks that include a dis- 

- 69 - 



continuity or by plate or radial jacking tests on larger in situ rock masses. 
Numerous test methods are described by Stagg. 8 

Dynamic testing of joints and fractures is a topic for research that has re- 
ceived little attention. Preliminary research indicates that joints fail by 
cumulative cyclic fatigue; therefore, confining pressure (depth of burial) is 
a critical factor in determining the residual strength of the failed joint. 109 
As confining pressure increases, rocks and joints demonstrate increasing 
ductility with a wide range of behavior, depending on rock type. The number 
of test cycles and the amplitude of deformation are both important in determining 
whether or not failure has been reached. 

An i sot ropy . Typically, site conditions can be modeled as transversely isotro- 
pic or, in other words, as horizontally layered. This vertical variation in 
properties may arise from natural layering, the tendency of density to increase 
with depth due to overburden pressure, downward penetration of weathering ef- 
fects, or presence of a water table. However, directional or horizontal aniso- 
tropy, a condition that is not usually considered, exists at some sites. Direc- 
tional anisotropy can be pronounced at sites underlain by dipping rock strata. 
For example, seismic waves traveling perpendicular to bedding planes will travel 
at a velocity that is the net effect of multiple layers and interfaces. This 
velocity is likely to be lower than the velocity measured parallel to bedding. 
Likewise, a preferred orientation of fractures might produce a directional 
variation in velocity. A thorough site investigation should include an effort 
to discern any significant anisotropy in dynamic properties throughout the site 
material s. 

Problems in Synthesizing Measured Properties 

When all the field and laboratory data for a site have been collected and 
reduced, representative site properties must be synthesized from results ob- 
tained from tests that are not directly comparable. For example, dynamic 
moduli calculated from resonant column tests are different from the results of 
laboratory cyclic triaxial tests or field seismic refraction surveys. Some 
standard procedures have been adopted for reconciling different results; however, 
they are not without difficulties. The chief factors accounting for these 



- 70 - 



differences are strain dependence of the properties and the stochastic nature 
of the data. 

Reconciliation of Site Properties . Laboratory tests offer advantages of close 
control of test conditions and ability to achieve high strains. However, it 
should be remembered that tests conducted on soil and rock samples do not 
perfectly model the behavior of soil or rock layers at a real site. Factors 
that place limitations on predictions of field behavior derived from laboratory 
tests are problems of sample disturbance and possible changes in sample struc- 
ture, boundary effects inherent in the testing apparatus, difficulties in 
reproducing the in situ state of stress, and representativeness of samples. 

Site properties are usually modeled using a combination of laboratory and field 
test data. Modulus values obtained from field geophysical surveys are taken to 

be maximum values {G ): laboratory test data are normalized to the low-strain 

max ' ' 

maximum moduli. However, as pointed out by Richart et al., 110 this procedure 
for determining moduli in situ has not been verified. It is not yet clear that 
linking field data and laboratory tests in this fashion yields accurate predic- 
tions of site response to earthquake shaking. Richart suggested that moduli 
in the field may, with increasing strain, undergo reduction less dramatic than 
the reductions observed in the laboratory. 

Strain Dependence . Seed and Idriss," Hardin and Drnevich, 111 and others have 
studied strain dependence of dynamic modulus and damping in laboratory soil 
tests. Shear modulus has been shown to decrease significantly with increasing 
strain in the range of 10 to 10~ 2 . Conversely, damping increases from 
several percent to 25% or 30% over the same range of strain. The studies 
cited above were carried out on cohesionless sands of standardized gradation 
and on several types of clays. Derivation of modulus reduction curves and 
damping curves for additional soil and rock materials is an important topic 
for future research. 

For laboratory dynamic testing of rock, strain-dependent properties cannot 
readily be generalized to in situ conditions because rock includes a wide range 
of materials in which the condition of the fractures and joints is frequently 
more influential in determining rock strength than are hardness, cementation, 

- 71 - 



etc., of the intact material. Extensive tests have been conducted on selected 
hard, fresh, rock cores. 101 Typically, these have been laboratory tests on cores 
of crystalline plutonic rocks, sandstones, and limestones. However, the results 
are of limited interest in earthquake engineering of underground structures be- 
cause failure in hard, strong rock is much more likely to occur at preexisting 
joints or fractures. More investigations are needed on the dynamic behavior 
of common sedimentary rocks such as shales, weak sandstones, and claystones; 
the influence of fractures should be included in such studies. 

The advantage of seismic geophysical methods is that they are capable of 
measuring properties throughout the entire soil or rock mass, including its 
discontinuities and inhomogenei ties. However, conventional field techniques 
usually permit evaluation of dynamic properties such as shear modulus only at 
strain levels well below 10~ 5 ; the results, then, are minimum or threshold 
values. A recently developed technique, a modified version of the crosshole 
seismic technique, has succeeded in obtaining higher strains, on the order of 
10" 5 to 10~ 3 . 97 ' 112 This method has not yet been applied to rock sites, and 
high setup costs are a severe limitation. 

Dynamic Properties as Stochastic Functions . In the future, site analysis may 
be called upon to address the statistical nature of the data synthesized 
to make the model as well as the implications for cost and safety calculations. 
The following is a simple illustration of the usefulness of probabilistic con- 
sideration of geotechnical data. 

Static tunnel stability is often presented in terms of a factor of safety 
that equals the ratio of driving forces to the forces resisting collapse. 
Both of these forces are estimated from test results and field observations 
and then viewed as deterministic values. If we calculate a factor of safety 
greater than 1.0, we say that on the basis of experience the hypothetical 
failure should not occur. In reality, a factor of safety slightly greater 
than 1.0 may or may not be a safe condition because our best estimates of 
joint orientations, joint plane friction angles, and in situ stress may err 
either on the conservative side or on the nonconservati ve side. Therefore, 
what is needed for analysis of critical facilities is a probabilistic estimate 
of safety. 

- 72 - 



A stochastic function is a mathematical model of a physical system that allows 
the variable of interest to take random values according to a prescribed 
probabilistic distribution. Baecher et al., for example, analyzed joint 
measurements from many excavations in rock and showed that joint length is 
best fitted by a lognormal distribution and that joint spacing is exponen- 
tial. 113 Similarly, density, modulus, and every other parameter that enters 
into the stability calculation could be modeled with a statistical distribution 
of values. From this information, a probability of occurrence and incurred 
costs could be calculated for every outcome or mode of failure. Underground 
seismic motion inputs needed for such a calculation could be derived with 
methods similar to those currently used to give probabilities of recurrence 
for accelerations at surface sites. 

Site dynamic properties are not usually viewed as stochastic functions, de- 
spite known biases and variations due to the measurement techniques employed 
and the frequent occurrence of natural inhomogenei t i es in soil and rock 
materials. However, seismic safety criteria for critical structures are 
becoming increasingly stringent, and future site investigations are likely 
to place increased emphasis on probability and risk calculations. 



- 73 - 



5. Seismic Wave Propagation 

The response of underground structures to seismic waves can be better under- 
stood by studying the theoretical and practical aspects of the propagation of 
the waves through the earth materials and the interaction of those waves with 
the structures. In this chapter, the general nature of underground motion is 
reviewed; particular attention is given to those factors that change the motion 
along the transmission path between the source and the site and at the site 
itself. Because the variation of motion amplitudes with depth is an important 
consideration at the site of underground structures, this subject is explored 
by a thorough literature review and some numerical studies. The chapter con- 
cludes with a detailed investigation of the interaction of seismic waves with 
a circular cavity in a half-space. 

THE NATURE OF UNDERGROUND MOTION 

Factors Affecting Underground Motion 

A number of factors contribute to the ground motion arriving at the location 
of an underground structure. A discussion of these factors can be facilitated 
by referring to Figure 25. The three basic components that determine the char- 
acteristics of ground motion to be expected at a given site are the source re- 
gion, the transmitting region, and the site region. 

Source Region . The source region consists of that part of the earth's crust 
immediately surrounding the earthquake source. This volume of the crust serves 
as the region of energy release from which seismic waves emanate in all direc- 
tions. Only a fraction of this energy will arrive at the site and contribute 
to the ground motion there. 

The factor that approximately defines the amount of energy injected into the 
crust by the earthquake is the magnitude of the earthquake. The magnitude is 
in turn affected by the extent (area) of faulting, the amount of strain energy 
stored in the earth prior to the earthquake, and the particular manner in which 
the stress is released (i.e., the faulting mechanism). 



- Ik - 




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The energy that is released is distributed among various types of seismic waves, 
There are surface waves, such as Rayleigh and Love waves*, whose amplitudes are 
largest near the earth's surface and diminish with increasing depth below the 
surface. There are also body waves, which consist of compression (P) and shear 
(S) waves. The amplitudes of body waves diminish as they spread out in all di- 
rections from the source of the earthquake. Body waves can be reflected by or 
refracted through boundaries between adjacent layers of material within the 
earth. Thus, seismic energy released by the earthquake source may travel by a 
number of wave types (or modes) and along a number of paths (see Figure 25). 

Faulting mechanisms and focal depth strongly affect the distribution of energy 
among the different types of seismic waves. For example, deep earthquakes tend 
to produce less surface wave energy than body wave energy. Furthermore, the 
wavelengths of the predominant surface waves tend to be somewhat greater for 
deep earthquakes than for shallow earthquakes. 

Transmitting Region . The transmitting region is that part of the earth's crust 
through which the seismic waves travel from source to site. This region modi- 
fies transmitted seismic energy by attenuating the amplitude of seismic motion 
through the process of geometrical spreading. This simply reflects the fact 
that the same amount of energy must pass through larger and larger volumes of 
material as it proceeds away from the source. For surface waves, the geometri- 
cal spreading factor is approximately proportional to \//k~~> where R is the 
distance measured from the source to the site along the path followed by the 
seismic waves. For body waves, this factor is proportional to \/R . Thus, as 
the seismic waves proceed outward from the source, geometrical spreading re- 
duces body wave amplitudes more quickly than surface wave amplitudes. 

The transmitting region also reduces the amplitude of seismic motion through 
absorption (anelastic attenuation). Because no medium is truly elastic, some 
energy is converted irreversibly to heat during each cycle of motion as the 
seismic wave proceeds through the medium. In general, except in the immediate 
vicinity of the source and in soil layers very close to the earth's surface, 



-See Appendix D for an explanation of these and other seismological terms 

- 76 - 



e.g., less than 300 ft (100 m) , this absorption mechanism is usually not sig- 
nificant. 

Finally, the distribution of seismic energy in the transmitting region may be 
modified through the presence of inhomogenei ties in the earth's crust. As 
waves spread out from the source in a spherically symmetric way, they are re- 
flected and refracted by discontinuities in the crust. Thus, the waves travel 
in many different directions, not just radially from the source. Depending 
upon the geometry of these structural discontinuities, there may be relative 
enhancement or dimunition of motion amplitudes at a given point, relative to 
what would exist in a homogeneous medium. Given the right shapes, a given por- 
tion of the earth's crust could behave exactly like an optical lens, producing 
a considerable focusing of energy. 

Elastic moduli and density generally increase with depth. Concomitantly, 
seismic wave velocities also increase with depth because increases in elastic 
moduli are usually greater than increases in density. Therefore, the earth- 
quake waves that propagate away from the source with downward inclination pass 
from layer to layer of material with increasing wave speed. This results in a 
refraction of the waves in such a manner that the wave paths appear curved and 
concaved upward as illustrated in Figure 25. 

In summary, the three factors that influence redistribution of seismic energy 
in the transmitting medium are distance traveled along the ray path by each 
wave type (geometrical spreading), anelastic attenuation, and spatial varia- 
tions in the properties of the earth material. 

Site Region . The site region consists of that portion of the earth's crust 
immediately adjacent to the underground structure. The response of the site 
to incoming seismic waves depends, in part, on the presence of soil layers 
overlying bedrock. In general, the seismic velocity in soil or similar pro- 
ducts of weathering is lower than that in the parent rock below. Thus, as the 
incoming energy slows down, it must "pile up," that is, generate higher ampli- 
tude seismic motion, in a manner analogous to t;hat in which ocean wave ampli- 
tudes increase upon approaching a beach. An additional property of near- 
surface soil layers is that they may trap energy in certain frequency inter- 



- 77 - 



vals through a resonance process so that motion amplitudes at select frequen- 
cies are enhanced, while amplitudes at nonresonant frequencies are diminished. 
The layers thus act as if they have a resonant frequency. This effect can 
occur in layers of significant thickness; for example, the alluvial layer 
underlying Mexico City has a resonant period of approximately 2.5 sec. 

The dependence of amplitude on depth is also a characteristic of the site 
region. The general amplification of seismic waves propagating from rock into 
soil as they approach the earth's surface is part of the physical explanation 
underlying the popular notion that seismic motion diminishes with increasing 
depth. The amplitude of surface waves generally diminishes with depth as well, 
also accounting in part for this popular observation. The predominant surface 
wave is the Rayleigh wave, whose amplitude varies with depth in an elastic 
half-space as shown in Figure 26. The Rayleigh wave motion in a real layered 
geology is much more complex, but the shape of the principal modes is fairly 
well represented by these curves. Considering a Rayleigh wave with a period 
of 0.5 to 1.0 sec and a velocity of 2,000 fps (610 m/sec) an underground open- 
ing at a depth of 100 ft (30 m) corresponds to a depth-to-wavelength ratio of 
0.05 to 0.10 (wave length = period x velocity). The curves in Figure 26 indi- 
cate that the horizontal amplitude of the Rayleigh wave may be significantly 
smaller at that depth but that the vertical amplitude may actually be larger. 

Another important factor in the depth-dependent phenomenon involves the reflec- 
tion of body waves off the free surface of the earth. Because the earth's sur- 
face is stress-free, the amplitude of the motion associated with a body wave 
reflected there is larger than (up to twice) that of the incident wave. Below 
the surface, both the incident and reflected waves are present, and their am- 
plitudes and phase relationships combine to produce a complex interference 
pattern that varies both with time and with depth. Theoretically, for a homo- 
geneous medium, there is a critical depth below which the amplitudes of verti- 
cally propagating body waves will be one-half of the surface amplitudes. From 
the surface down to the critical depth, peak amplitudes are less than the sur- 
face values but do not necessarily decrease monotonical ly with depth. 

The exact behavior of motion amplitude with depth depends upon the time dura- 
tion of the wave train, its velocity in the medium, the angle at which the wave 

- 78 - 



Richart, Hall, Wood, Vibrations of Soils and Foundations , 

© 1970, p. 89. Reprinted by permission of Prentice-Hall, 

Inc., Englewood Cliffs, New Jersey. 




-0.6 -O.k -0.2 



0.2 0.4 0.6 
Amplitude at Depth 
Amplitude at Surface 



NOTE 



v is Poi sson' s rat io. 



Figure 26. Amplitude ratio versus dimensionless depth for 
Rayleigh wave. (Adapted from Reference 11*t.) 



79 - 



train approaches the surface, and the characteristics of the time history of 
the approaching seismic wave. This effect is treated in detail later in this 
chapter. 

Finally, the response of the underground structure itself must be considered, 
as described in Chapter 4. The response will be a function of the manner in 
which the immediate vicinity of the opening is excited or shaken, along with 
such factors as the size and shape of the opening, type of rock support, condi- 
tions of the surrounding rock or soil, damping, and depth below ground. 

Prediction of Underground Motion 

Problems Created by Lack of Recorded Motion . Very few records of strong motion 
in mines and tunnels are available due to a lack of adequate instrumental cover- 
age. Without the actual recorded motion in underground structures where damage 
has been reported, there is no basis for empirical estimates of the relations 
between structural damage, associated ground shaking, and such common earthquake 
parameters as magnitude and epicentral distance. 

The absence of we 1 1 -documented empirical correlations forces the engineer and 
seismologist to use some type of modeling technique to predict the response of 
an idealized form of the underground structure. However, the theoretical 
models representing underground structural response have not been verified by 
recorded ground motion, and the validity of the predicted response is very much 
in doubt. One solution to these problems is to substantially increase ground 
motion recordings in and around underground structures so that both the empiri- 
cal and theoretical approaches are effective predictors of potential damage and 
can be used to make recommendations for remedial action. 

General Descriptions of Prediction Approaches . Predicting the response of an 
underground structure located at some particular epicentral distance from a 
hypothetical earthquake begins at the source region by postulating a certain 
magnitude event. The most sophisticated way to proceed is to model the earth- 
quake source mathematically using such parameters as fault length, focal depth, 
and rupture velocity. The outcome of such a model study would be a fairly com- 
plete description of the radiation pattern of seismic energy emanating from the 
fault region. This radiation pattern would contain information about the 

- -86 - 



amount of seismic energy of each wave type (P, S, Rayleigh, Love) and its 
directional distribution relative to the source. The accuracy of such a 
description would be dependent on the accuracy of the faulting model and on 
knowledge of the surrounding crustal structure. Next, the wave paths to the 
site could be traced, using known laws of reflection, refraction, and attenua- 
tion, with a model of the crustal structure between the source and site regions. 
The outcome of such a calculation would be a fairly complete description of the 
seismic wave field at the location of the underground structure. A mathemati- 
cal model of the underground structure and the surrounding rock mass would be 
required to complete the problem. The response of the model of the structure 
and rock mass to the seismic wave field would be the subject of interest to the 
engineer concerned with design. 

A far more simplified approach avoids sophisticated mathematical modeling of 
the source, transmitting, and site regions; however, this ground motion char- 
acterization is almost devoid of detail. The simplified approach would use an 
assumed earthquake magnitude and an epicentral distance in conjunction with the 
large number of empirical distance-attenuation relations that have been derived 
from numerous ground motion recordings to arrive at an estimate of peak ground 
motion parameters (such as acceleration, particle velocity, and displacement) 
at the site of the underground structure. Peaffc --ground motion parameters can 
then be used with empirical correlations to predict cavity response (such as 
the use of damage correlations developed by Dowding and Rozen 17 > 25 to predict 
tunnel damage) . 

This latter approach to underground motion prediction is in extreme opposition 
to the former approach. The former approach provides a virtually complete 
mathematical description of the theoretical motion of the structure, while the 
latter approach provides only estimated values (those based on empirical rela- 
tions) of peak acceleration, particle velocity, or displacement associated with 
the free-field motion in the vicinity of the structure. 

Other approaches to estimating or predicting underground motion at the site 
might involve use of a "typical" seismogram corresponding to the epicentral 
distance under question. This seismogram would describe the time history at a 
point on the earth's surface directly above the underground site. Then, using 

- 81 - 



techniques described later in this chapter, the seismic wave field for all 
points below the surface could be estimated and used to excite the response of 
the underground structure. 

DEPTH-DEPENDENCE OF UNDERGROUND MOTION 

The nature of subsurface seismic motion in comparison with surface motions and 
with respect to its variation with depth has been discussed in general terms. 
To further clarify the manner in which depth influences underground motion, the 
literature of observational research and theoretical studies is reviewed in 
this section. In addition, numerical studies are conducted to explore the in- 
fluence of the duration and characteristics of the time history and the effect 
of varying the angle of incidence to the ground surface. 

Literature Review 

Considerable work has been done on selective amplification of seismic waves in 
near-surface soil layers by Japanese researchers. 115-122 In general, their 
efforts have been directed toward understanding the effects of near-surface 
soil conditions upon surface ground motion. Their reports have been largely 
observational and descriptive, although mathematical studies were presented in 
some. Shima 121 compared earthquake records at the surface with those in two 
boreholes at depths of approximately 66 ft (20 m) . The site geology consisted 
of sand and clay layers over gravel. Shima found that the predominant frequen- 
cies in the surface records were explained by the multiple reflections of the 
waves that occurred in the strata above the gravel bed. Kanai et al. 122 com- 
pared records obtained with surface geophones with those obtained with near- 
surface geophones and attempted to model the data in terms of the multiple re- 
flections in the alluvial soil layers. They considered four sites of various 
subsoil conditions, generally consisting of layers of sand, clay, and silt over 
rock. The deepest geophone at each site was at 72.8 ft (22.2 m) , 120.7 ft 
(36.8 m) , 122.4 ft (37-3 m) , and 171-9 ft (52.4 m) . The results indicate that 
in certain frequency intervals (corresponding to the natural frequencies of the 
soil system) there is selective amplification of seismic waves and that the 
high-frequency components, in general, attenuate more rapidly with depth than 
do the low-frequency components. 



- 82 - 



Similar studies have been conducted in the United States. Data from a 102-ft 
(31-m) downhole array in Union Bay (Seattle), Washington, were analyzed by Seed 
and Idriss 123 and others. 121+ ' 125 Joyner et al. 126 collected data from a down- 
hole array on the shore of San Francisco Bay in California, the deepest mon- 
itoring point being 6.6 ft (2 m) below the top of the bedrock at a depth of 
610 ft (186 m) . Recorded surface motions were compared with surface motions 
predicted by a simple plane-layered model. They found that simple plane- 
layered models are capable of giving reasonably good approximations of the ef- 
fects of local soil conditions for low-amplitude ground motion. 

The amplification of seismic waves by near-surface soil layers and the expla- 
nation offered by multiple reflection theory were reviewed by Blume 127 and 
Okamoto. The general acceptance of this phenomenon is reflected by the cur- 
rent technology for predicting the dynamic response of soil systems as reviewed 
in Chapter 4. 

Researchers have given some attention to earthquake motion at depth, specifi- 
cally in rock. A series of papers by Kanai et al > 117_119 > 122 utilized low- 
intensity motions recorded in the Hitachi copper mine at depths of 492 ft 
(150 m) , 984 ft (300 m) , and 1 ,476 ft (450 m) . It should be noted that the 
principal intent of these papers was to obtain an understanding of the nature 
of surface motion that was recorded at an alluvial site approximately 1,000 ft 
(300 m) away. However, for this discussion, the motions recorded at depth are 
of interest. The horizontal displacement at the 1 ,476-ft (450-m) monitoring 
point was larger than the displacements above it at some instances of time. 
Furthermore, the peak amplitude at 1,476 ft (450 m) for the entire time history 
was often of the same order of magnitude as the peak amplitudes above. These 
records reveal a complexity in the nature of the motion at depth in rock and 
do not support a definitive statement on the attenuation of seismic amplitudes 
with depth. 

Okamoto 33 reported on a study for which motions were recorded at the surface 
and at depths of 56.4 ft (17.2 m) , 112.2 ft (34.2 m) , 168.0 ft (51.2 m) , and 
220.5 ft (67.2 m) in a vertical shaft at the Kjnugawa Power Station. The 
geology of the site consisted mainly of hard, coarse-grained tuff. There was 
almost no difference in displacement between the ground surface and the bottom 

- 83 - 



of the shaft; however, accelerations in the upper stratum were 1.5 to 2.5 times 
those of the lower stratum. 

Similar results were obtained in a study of accelerograms recorded at a rock 
site during the 1976 Friuli earthquake sequence. 128 That study also found that 
peak accelerations recorded at the surface are normally much higher than those 
recorded simultaneously at depth. The Fourier spectra of the deeper recordings 
appear smoother and flatter than those of the surface recordings. An important 
finding of that study is that significant amplifications of bedrock accelera- 
tions may be recorded on the outcrop of a rock mass if the outcrop is heavily 
weathered at the surface. 

It should be noted that some of the underground motions discussed above were 
recorded in tunnels or power plant caverns; however, this was apparently done 
for the convenience of obtaining an underground recording site rather than in 
an attempt to observe behavior specific to an underground opening. Some recent 
observations have been conducted in three power plant caverns by Ichikawa. 129 
The purpose of those observations was to not only clarify the characteristics 
of motion with depth but also to determine the behavior of an underground 
cavity during seismic motion. The observations revealed that the horizontal 
motions of the two sidewalls were in phase for some earthquakes and out of 
phase for others and that the vertical motions were always in phase. 

The results of ongoing work by Iwasaki on underground seismic motion at four 
sites around Tokyo Bay 120 may begin to clarify the differences between earth- 
quake motion recorded in rock as opposed to that recorded in alluvium. Three 
of the sites — Futtsu Cape, Ukishima Park, and Ohgishima — are typical allu- 
vial deposits of sands, silts, and clays, while the fourth site, Kannonzaki , 
may be characterized as soft rock, consisting of layers of sandstones and silt- 
stones. The deepest borehole accelerometer at each of these four sites is at 
361 ft (110 m) , 417 ft (127 m) , 492 ft (150 m) , and 394 ft (120 m) . Iwasaki 
has recorded a sufficient number of earthquakes at these sites to begin to 
describe statistical trends. 130 

For Ukishima Park (one of the alluvial sites), the mean value of the two hori- 
zontal components of acceleration recorded at 417 ft (127 m) is approximately 



- 84 - 



one-third of the mean value for the surface. Individual records do not vary 
greatly from this mean; the mean value plus and minus one standard deviation is 
between one-half and one-quarter of the surface mean. Thus, it would appear 
that at Ukishima Park peak horizontal accelerations at the surface are ampli- 
fied approximately two to four times those at depth. This observation is con- 
sistent with both theoretical and observational studies of alluvial sites. 

The data obtained at Kannonzaki (the soft rock site) are very different from 
those obtained at Ukishima Park. The mean value of the two horizontal compo- 
nents of acceleration recorded at 39^ ft (120 m) at Kannonzaki is 80% of the 
mean value for the surface. Furthermore, individual records vary rather mark- 
edly from this mean, with peak accelerations at depth greatly exceeding peak 
surface accelerations for some earthquakes. This is reflected by a very large 
standard deviation, and the mean value plus and minus one standard deviation 
varies between 132% and 28% of the surface mean. This suggests that, for 
fairly uniform rock sites, peak accelerations are not, in general, signifi- 
cantly reduced at depth as compared with peak accelerations at the surface. 
However, individual earthquakes may result in accelerat ions at depth that are 
either significantly larger or smaller than the surface accelerations. 

A recent paper by Nakano and Kitagawa indicates that there are approximately 
200 instruments for recording underground motion in Japan at this time. 131 
About 5% of these are actually at the ground surface, 57% are between the sur- 
face and a depth of 66 ft (20 m) , and 28% are at depths between 66 ft (20 m) 
and 197 ft (60 m) . Thus, 90% are within 197 ft (60 m) of the ground surface. 
The shallow depth of most of the seismometers and the fact that many are 
located near buildings indicate that the purpose of this instrumentation is 
primarily for the analysis of soi 1 -structure interaction. At this time, only 
two seismometers are located below 660 ft (200 m) -- one at about 1,000 ft 
(300 m) and the other at about 11,500 ft (3-5 km). 

These studies of recorded motion, as well as observations by miners underground 
during earthquakes, 16 ' 32 tend to substantiate the notion that motion does re- 
duce with depth. Unfortunately, the data are not sufficient to provide quanti- 
tative predictions of the reduction. Furthermore, in some cases the data re- 
veal an increase in motion with depth. 

- 85 - 



Underground motion predictions by mathematical models have been compared with 
actual recordings, but the extent of agreement has depended upon the sophisti- 
cation of the model and the complexity of the site geology. As previously 
noted, the models that assume shear waves propagating vertically through hori- 
zontal layers have provided good agreement with records from sites with hori- 
zontally layered soil deposits. 120 ' 122 " 126 A very simple model has sometimes 
been suggested in which a vertically propagating body wave is represented by a 
single sinusoidal pulse of length equal to the wavelength. Such a model pre- 
dicts that underground motion (in a half-space) reduces to one-half of surface 
value at depths greater than one-fourth the wavelength. However, such results 
are meaningless because the pulse is an oversimplified model of typical earth- 
quake motion. O'Brien and Saunier have developed a fairly sophisticated 
model that includes P- , SV-, and SH-waves propagating upward at various angles 
of incidence in a medium consisting of a single horizontal layer over a half- 
space. Their model should be more representative of horizontally layered sites 
than previous models. Unfortunately, their comparison of predicted motion with 
recorded motion was not very satisfactory because the model did not represent 
the actual site geology. 

Theoretical Formulation of Depth Dependence 

The depth dependence of seismic motion due to incident horizontally polarized 
shear (SH) waves in a homogeneous, isotropic, perfectly elastic half-space is 
considered below. There is a loss in generalization by considering only SH 
waves and ignoring vertically polarized shear (SV) waves and compressional 
waves. However, it is justified for this study because it permits the easy 
evaluation of underground motion without the complications introduced by cou- 
pl ed waves . 

We begin with a brief discussion of the mathematical model to be used in this 
study. Consider a point located at a depth x 2 below the free surface of a 
homogeneous, isotropic half-space with S-wave velocity $ (see Figure 27). 

The general equation governing the displacement in a homogeneous, elastic medium 
is 



= (X + y)v(V • u) + yV 2 w (21) 



d 2 u 
U 2 

- 86 - 




Figure 27. Schematic of coordinate axis, incident and 

reflected wave fronts at arbitrary angle of 

incidence, and surface control point. 



87 - 



where p is the density of the medium, u is the displacement vector, and X and y 
are the Lame constants of the medium. 

For SH motion, Equation (21) reduces to the simple scalar form: 

dhi. 



■3 



= ^ V 2 w 3 (22) 



where 3 2 = — • 

P 

The displacement component u$ describes the anti plane component of the motion 
defined in the plane of X\ and x 2 as shown in Figure 27. Consider SH body 
waves incident at angle 6 to the free surface {x 2 - 0) . This assumes that the 
source of the motion is sufficiently removed from this region to allow wave 
front curvature to be neglected. Using the Fourier transform of u$ defined as 

U^(xi,x 2 ,^) = I u$(xi,X2,t)e W dt (23) 



»/ — 00 



A solution for the displacement field at point (x^,x 2 ) may be written in the 
form 



L."* 



•n.'W n .11) " . n ill) 

•x\s i n6+i — X2COS6 - i — sr^s i n8- i — a^cosS . , 
U 3 = U x e p 3 + A 2 e B 6 Je ,wt (24) 



where to is the angular frequency of the motion, $ is the shear wave velocity 

{V ) in the medium, and i = /-I. The angle 6 is the angle of incidence of the 

s 

impinging wave measured counterclockwise between the outward normal to the free 
surface and the normal to the incident wave front. The factors ^i and A 2 are 
amplitudes of the waves impinging on and reflected from the free surface, re- 
spectively. Application of the stress-free condition at x 2 = implies that 
Ai = A 2 . Thus, with the help of trigonometric identities, we may write 



U 3 {x 1 ,x 2 ,^) ij i ^x 2 cosQ -\jx 2 cos( 



tf 3 (0,U,o>) 



I — X2COS8 

e + 

fa a\ 

= cos [ — x 2 cos 9 Je 

- 88~ - 



- 1 -£X\S in6 
* 3 (25) 



.w 
- 1 -£-#is ml 



Alternatively, we can take the ratio of U^{xi,X2,oi) to #3(0)) , the part of the 
incident displacement that is independent of the spatial variable, namely 

4(a)) = ^ie iw * (26) 

Since £/ 3 (0,0,u)) = 2£/ 3 (w), Equation (25) becomes 

U z {x l ,x 2 ,u) / \ -i^xsine 

= 2 cos [- X2 cos e)e (27) 



^3(00) 



(I *2 cos ej 



Equation (27) gives the displacement of the SH component in terms of the inci- 
dent SH motion as a function of frequency, depth, wave velocity, and angle of 
incidence. This ratio applies to the case for which the incident wave consists 
of a harmonic wave of infinite duration, and thus is a frequency-domain trans- 
fer function, relating the motion at depth to that of the incident wave field 
for a frequency oi. Note that substitution of xi = in Equation (27) gives the 
familiar effect of amplitude doubling of the incident motion due to reflection 
at a free surface of SH-waves. 

The literature has sometimes reported that amplitudes at depth are one-half 
those at the surface; that statement, however, is oversimplified and misleading. 
Equation (25) shows that the amplitude at depth is not half that at the surface. 
There are an infinite number of depths at which the motion is reduced to one- 
half its surface value because the incident wave field is assumed to be of 
infinite duration. Thus, the interference pattern described by Equation (25) 
is stationary. 

Consider now the general problem in which the wave field consists of a dis- 
placement time history of arbitrary time dependence. In general, this wave 
motion will be composed of all frequencies, each with its appropriate amplitude 
and phase. Let u®(Q,0,t) be the displacement time history of this wave train 
at the free surface. Then, to find u^{x\,X2,t) at point {x\,X2) , we first com- 
pute f/ 3 (0,0,t), the Fourier transform of u®, by Equation (23). 



- 89 - 



Then, £73(0,0, co) is multiplied by the frequency transfer function given by 
Equation (25) to obtain #3 {xi ,x 2 ,u>) . Finally, w 3 {xi ,x 2 ,t) is obtained by the 
inverse Fourier transform of U$ (xi ,x 2 ,u) , given by: 

u^ixi ,x 2 , t) = ■=— / ^3(^1 ,x 2 ,u)e dm (28) 



2tt / 



The same general procedure would be followed for the xi and x 2 components of 
the motion (i.e., P and SV) , though the details would be somewhat more com- 
plicated because these motions are coupled upon reflection from the free 
surface. 

So far, we have discussed the depth dependence as a function of the frequency 
content of the incident wave field, which relates the amplitude at depth to 
that at the surface for each frequency. The amplitude of the incident wave 
field is, of course, a function of magnitude, epicentral distance, etc. The 
effect of duration is not resolved by the transfer function represented by 
Equat ion (25) . 

Referring to Figure 28, consider now the case where the leading edge of a wave 
train of finite duration, Tq , has just reached the free surface at point A. 
The length of the wave train in space is Lq = Tq&. The reflected wave will 
travel down along path AC at the same time that the trailing edge of the 
wave train is approaching the free surface along path BC . There will be a 
critical depth, Y , at which the reflected wave and the end of incident train 
arrive at point C at the same time. From Figure 28, AC = BC = L = Y /gos 6, 
and L Q = L (1 + cos 26), But £0 = P r » so that the critical depth is given by 

3T_ cos 6 &T. 

j = °- = °— (29) 

e (1 + cos 29) 2 cos 6 

Beyond this critical depth, no interference is possible; therefore, the ratio 
of the peak amplitude at depth to the peak amplitude at the surface will be 
one-half for all x 2 > Y . In general this ratio is greater than one-half for 
depths above the critical depth (that is, for x 2 < Y ). However, if large 
peaks of comparable magnitudes but opposite signs exist in the incident and 



- 90 - 




u- 




O 




<D 




O 




c 


• 


<u 


to 


1_ 


c 


0) 


•— 


M- 


TO 


l_ 


l_ 


<u 


4-1 


+-J 




c 


<u 


■— 


> 




fO 


l_ 


2 


o 




M- 


"O 




(1) 


.c 


4-» 


+-» 


o 


Q. 


<u 


<U 


p— 


-o 


<4- 




0) 


i— 


l_ 


(D 




O 


■o 


•— 


c 


4-1 


A3 


l_ 


+J 


C_> 


c 




a> 




■o 


■ 


•— 


oo 


o 


CM 


c 


<U 




l_ 




3 




O) 





- 91 



reflection waves, it is possible to have occasional isolated depths above the 
critical depth where, for a particular earthquake record, the amplitude ratio 
is less than one-half due to destructive interference. Thus, the precise be- 
havior of the amplitude ratio above the critical depth is a function of the 
detailed nature of the incident time history. 

Parametric Studies of Depth Dependence 

A computer program has been written that will input a displacement time 
history for the surface ground motion and then calculate the corresponding 
displacement and strain at any point at depth. The program considers only 
plane SH-waves in a homogeneous, isotropic half-space. The origin of coordi- 
nates is taken at the surface recording point, with X\ being the horizontal 
axis and x-i the vertical (depth) axis. The program will handle arbitrary angle 
of incidence of the wave front (i.e., 6 = 0°, vertical incidence, to 9 = 90°, 
horizontal incidence). The main input parameters are the shear wave velocity 
in the medium, the depth of the observation point, the distance off the 
vertical axis of the observation point, the angle of incidence of the plane 
wave, and the time history of the ground motion (at the origin). 

The program is structured to allow expansion of its capabilities at some time 
in the future. The next step would be to include layering in the media as well 
as three-dimensional body wave input (i.e., P, SV, and SH) , with the resultant 
three-dimensional response. Material damping, which involves the use of a com- 
plex material modulus, may be easily incorporated into the program. This can 
be readily accomplished by adding an imaginary part to the shear wave velocity 
in evaluating the transfer function given by Equation (25). 

Study Using a Simple Pulse . To investigate the variation of seismic wave 
motion with depth, a simple parametric study was conducted considering a hori- 
zontally polarized, plane shear wave traveling in a half-space with shear wave 
velocity, 3, and incident to the free surface at an arbitrary angle, 9 (see 
Figure 27) . 

So as not to obscure the information contained in the parameter variation, a 
simple wave form of finite duration was chosen as the surface control motion. 



- 92 - 



The wave is represented by 
fit) = 1 



8/J . / zu \ . 2 / nt \ r n . m 
_ sm (_) sm 2(_J forO<t<T ^ o) 



otherwise 



The derivatives and integrals of f(t) exist and are well behaved; that is, there 
are no discontinuities or residuals to make calculations difficult to interpret. 
The motion at the surface is then specified as 

u 3 (xi,0,t) = u 3 0p f(t) (3D 

where u$ " = [w 3 (0,0,t)] . , the peak value of the motion at the control point 
(0,0). 

Two parameters were varied, the depth of the observation point and the angle of 
incidence of the incoming wave. For this study, the wave form was discretized 
into 30 equally spaced time intervals of 0.02 sec, resulting in a wave train of 
0.60-sec duration (Tq) . A constant shear wave velocity of 2,000 fps (609-6 m/sec) 
was assigned to the medium. Using these values of wave train duration and shear 
wave velocity, we obtain a critical depth of 600 ft (182.9 m) for a vertically 
incident wave (e = 0°) and a critical depth of 693 ft (211.2 m) for a wave inci- 
dent at 6 = 30°. 

To observe the variation with depth of the input wave motion, the displacement 
and strain time histories were computed at five separate depths, x^ = 100, 200, 
400, 600, and 1,000 ft (30.5, 61.0, 121.9, 182.9, and 30^.8 m) , and for two 
angles of incidence, 9=0° and 30°. The depths were chosen to bracket the 
critical depth in order to observe the effect of the interference of the inci- 
dent and reflected wave trains. 

The first case considered is that of a vertically incident wave (6 = 0°). The 
time histories of the displacement, u% y and of the strain component", 632, have 
been computed for each of the designated depths and are presented in Figures 29 
and 30, respectively. The displacement time histories (Figure 29) clearly show 



"The strain component e.. is the shear strain between the x. and x. directions, 



- 93 - 



op 



(di mens ionless) 




NOTE: 1 ft = 0.301*8 m. 



-1.0 1.0 
Time, t (sec) 



Figure 29. Displacement time histories at depth for 
vertically incident wave (6=0). 



9*» 




NOTE: 1 ft = O.3C48 m. 



-1.0 1.0 

Time, t (sec) 



Figure 30. Strain component, e , time histories at depth 
for vertically incident wave (0 = 0°). 



- 95 



the effects of depth. The incident and reflected wave trains are completely 
separated below the critical depth, resulting in the wave amplitude always being 
one-half the surface amplitude depth. For the chosen wave form, the ratio of 
the amplitude at depth to the surface amplitude gradually reduces from a value 
of one at the surface to a value of one-half upon reaching the critical depth. 

The strain component £32 time histories monitored at the same depths are dis- 
played in Figure 30. (Note: £32 = at the surface due to the stress-free 
boundary condition, and e 31 = at al 1 points because 6 = 0°.) Again, the 
separation between the incident and reflected wave trains below the critical 
depth is clearly observed. This figure illustrates the nonuni formi ty of the 
reduction of amplitude with depth. Here the amplitude of the £32 strain compo- 
nent at the 200-ft (61-m) monitor point is clearly larger than the amplitude at 
the 100-ft (30.5-m) monitor point. Note also the sign change in the £ 32 strain 
component between the incident and reflected wave trains. 

The wave form incident to the free surface at 6 = 30° is shown in Figure 31* 
The displacement time history at the surface is assumed to be the same as that 
for the vertically incident wave. The displacement time history at depth is 
similar to that for the vertically incident wave, except that the amplitude re- 
duction near the surface is less for the wave incident at 9 = 30°. At Xz = 
100 ft (30.5 m) there is a 26% reduction in amplitude from the surface ampli- 
tude for 6=0° incidence and a 20% reduction for = 30°. Figure 32 displays 
both components of strain e 31 and £32 for a wave incident at = 30°.* Here 
both the £3! and £32 strain components do not exhibit a uniform reduction of 
amplitude with depth. The amplitude of the £31 component at the 400-ft (l21.9 _ m) 
monitor point is 100% larger than the amplitude at the 200-ft (61-m) monitor 
point. Similarly, the amplitude of the £ 32 component at the 200-ft (61-m) 
monitor point is 30% greater than that at the 100-ft (30.5~m) monitor point. 

The variation of displacement and strain with angle of incidence is shown in 
Figures 33 and 3^. The monitoring point was taken off axis at x\ = -100 ft 



*£ 32 = at the surface. c 31 ^ at the surface and is double the incident 
strain pulse. 



- 96 - 



(d i mens i on less) 




NOTE: 1 ft = 0.3048 m. 



1.0 


Incident Pulse 
/ Reflected Pulse 

A /f 


0.5- 





1 / 


-1.5 


1/ 1/ 


-1 .0. 




1 







-1.0 1-0 
Time, t (sec) 



Figure 31. Displacement time histories at depth 
for wave incident at 6 = 30 . 



97 - 



Strain, e /u P 

(io" 2 /ft) 



Strain, e /u, ^ 

(io" 2 /ft) 




NOTE: 1 ft = 0.30ll8 m. 



-1.0 1.0 

Time, t (sec) 



•1.0 1.0 

Time, t (sec) 



Figure 32. Strain components, e and e , time histories for 
angle of incidence 6 = 30 . 



- 98 - 



(dimens ionless) 




NOTE: 1 ft = 0.30148 



Figure 33. Displacement time histories at the same monitoring point for 
variable angle of incidence of incoming wave. 



- 99 - 



Strain, c^/u^P 

(io" 2 /ft) 



Control Motion 



Strain, £ 31 /" 3 



(10 /ft) 




NOTE: 1 ft = 0.3048 m. 



1.0 

Time, t (sec) 



1.0 

Time, t (sec) 



Figure 3k. Strain components, e 31 and e 32 , time histories at the same 
monitoring point for variable angle of incidence of incoming wave. 



- 100 - 



(-30.5 m) and at x 2 - 100 ft (30.5 m) , and the displacement and strain time 
histories were calculated for angles of incidence of 9 = 0°, 30°, 60° , and 90°. 
The displacement time history (Figure 33) for 6 = 90° shows no reduction in 
amplitude because there is no reflection off the free surface and consequently 
no interference of incident and reflected wave trains. There is a reduction in 
amplitude as the wave front approaches the vertical angle of incidence, where 
it is reduced to approximately 80% of its surface value. 

Study Using an Earthquake Time History . To observe depth effects with an actual 
earthquake time history, the Temblor N65W record of the 1966 Parkfield earth- 
quake was chosen as the surface control motion. The record was of particular 
interest due to several factors: it was a free-field rock site recording at a 
hypocentral distance of 9-9 miles (16 km), it had a relatively high horizontal 
peak acceleration of 0.27g for a magnitude 5.6 event, and it displayed approx- 
imately 1.5 sec of ground acceleration equal to or greater than one-half the 
peak ground acceleration. The raw acceleration was fitted with a parabolic 
baseline connection and integrated twice to obtain the ground displacement. The 
first 22.72 sec of record were analyzed, and the displacement time history cal- 
culated for the depths is given in Figure 35, assuming 9=0° and 3 = 2,000 fps 
(609.6 m/sec) . 

The interference between the incident and reflected wave trains can be observed 
in Figure 35* The two wave trains are completely superimposed on each other at 
the ground surface, resulting in a doubling of displacement amplitudes at the 
surface. Another way to view this is to observe that the two wave trains sepa- 
rate with depth so that below the critical depth the amplitudes are one-half 
those at the surface. However, the peak displacement amplitudes do not reduce 
uniformly with depth. In this example, the peak amplitude is reduced by 5% at 
a depth of 1,000 ft (305 m) and by }h% at 4,000 ft (1,219 m) . At 8,000 ft 
(2,438 m) it is still only reduced by lk%. At 12,000 ft (3,658 m) it is reduced 
to 50%, but at 16,000 ft (4,877 m) it is increased, with only a 3U reduction 
from the surface value. This nonuniformity in the reduction of amplitudes with 
depth is due to the interference between different peaks in the incident and 
reflected waves. Clearly, then, the spatial arrangement of the peaks within 
the time histories have an important influence on the reduction of amplitudes 
with depth. 



- 101 - 











Displacement, U- 










2.0" 


jT~- Peak = 


.861) 








1 .0- 


h * 










» i o- 


A 






1 \ / 










yS -1.0- 


1/ 










yr -2.0. 


, y 








1 t 






yr 2.0" 












>^ i 0- 


h „ 




Z] 






X 


-J\ A- 






l.OOO' 




-2.0. 


V 

Peak = -1.780-V 
1 r 














2.0" 








li.OOO' 


-*■ 


i.o- 


M\ A^ 










• .E 0- 


-nii\ r 










-1.0- 
-2.0- 


V 

Peak = - 1 . 237 — ' 

1 1 










2.0 








8,000' 




1 .0- 

• i °" 


— Ai^y 


A 










12,000' 




-1 .0- 
-2.0. 


V 

^Peak = - 

1 1 


1.225 








2.0 
1.0- 

• .E °" 


Peak = 0.932 


'V- 














-1 .0- 


V v w 






16,000' 




-2.0_ 


1 1 










2.0 

"""— — — ~ '"°~ 
* .E 0" 


Peak = 1 . 288\ 










-AA 


r^ 








-i.o- 


v V 






20,000' 




-2.0 








1 1 




2.0 


Peak = 0.932 

/ \ 

m m 
















• .E °" 


A/A 


r- 




Critical Depth 




-1 .0- 
-2.0 


V V 

1 1 






2<(,000' 








1 1 






2.0 


Peak = 0.932 
/ \ 
m tn 
















' — • i o 

*2 " 


VA 


f 








1 -1.0 


%V * 


/ 


10TE : 1 


in. = 2.5<l cm- 1 f 


C ■ 


0.30<l8 m. -2.0 


'111 


1 




1 1 1 1 


1 




10.0 0.0 10. 20. 

Time, t (sec) 


30. 



Figure 35. Displacement record of the 1 966 Parkfield (California) 
earthquake monitored to below the critical depth. 



- 102 - 






Nonuni formi ty in the reduction with depth is very clearly observed by the 
plot of peak displacement with depth in Figure 36. For purposes of comparison, 
the acceleration time history for the Temblor N65W record was also analyzed, 
and the variations of peak acceleration with depth are plotted to a depth of 
1,000 ft (305 m) . Although the peak acceleration drops to nearly one-half the 
surface value at a depth of 100 ft (30.5 m) , it increases again substantially 
at 400 ft (121.9 m) . For this particular record, where almost all the high 
peaks in the acceleration time history occur within a 2-sec interval, the 
peak accelerations below 1,000 ft (305 m) remain approximately one-half the 
surface value. However, for acceleration time histories with major peaks over 
an interval of many seconds, a much slower trend in reduction with depth is 
found. 

This parametric study shows that it is not possible to make a general statement 
about the amount of reduction that occurs with depth. There is some point, 
called the critical depth in this report, below which the incident and reflected 
body waves will not interfere. In the case of a homogeneous, elastic half-space 
the peak motions below the critical depth will be one-half the peak motions at 
the surface. The critical depth depends upon the duration of the strong motion, 
Tq , the wave velocity, and the angle of incidence, 6. For SH-waves, the critical 
depth is given by Equation (29). When considering a realistic earthquake record 
at the surface, such as the Temblor record for the 1 966 Parkfield earthquake, 
this study showed that peak motions may decrease with depth at first and then 
increase again before finally reducing to one-half at the critical depth. Fur- 
thermore, the critical depth might be extremely deep -- in this example, 22,720 
ft (6.93 km) for a duration of 22.72 sec. The variation of the maximum ampli- 
tude with depth (between the surface and the critical depth) and the complexity 
of the wave form will greatly depend upon the character of the surface record 
used in this type of study. 

When considering shallow depths -- say within 300 ft (100 m) of the surface — 
in homogeneous materials, this study shows little reduction. This finding agrees 
with the data reported by Iwasaki et al. 120 for a Tokyo Bay site (Kannonzaki) 
which consists of fairly homogeneous rock layers from the surface to the deepest 
monitoring point. Thus, when considering a site that is fairly homogeneous with 



- 103 - 



[ "3] peak /"3° P 



t"3W/»3° P 



5,000 



10,000 • 



Q. 
Q 



20,000 




500 - 



Critical Depth 



0) 



1,000 




Ratio of peak acceleration 
at depth to peak accelera- 
tion at the surface 



a. Ratio of peak displacement at 
depth to peak displacement at 
the surface 



NOTE: 1 ft = 0.3048 



m. 



Figure 36. Variation of peak displacement and peak acceleration 
with depth for the 1966 Parkfield (California) earthquake. 



104 - 



depth, the reduction in amplitude with depth is expected to be very small for 
body waves. 

This parametric study did not consider the effect of surface layers on ground 
motion. Soil layers, particularly soft soils overlying hard rock, are respon- 
sible for large reductions in peak motion with depth. Actually, the inverse 
statement better describes the situation. Soil layers amplify the incoming inci- 
dent wave as it propagates upward from the bedrock, resulting in very large 
amplifications of peak motion at the ground surface as compared with those in 
the bedrock. It is well known that the peak surface motions for soil sites are 
associated with the frequencies in the wave that correspond to the natural fre- 
quencies of the soil system. Most reductions in peak ground motion recorded at 
depth are undoubtedly due to near-surface geology, such as layering. 

DYNAMIC RESPONSE OF UNDERGROUND CAVITIES 

This section deals with the dynamic response of a two-dimensional cavity in 
an elastic half-space. The cavity is circular in cross section. Its axis lies 
at a finite distance from and parallel to the free surface of the half-space. 
The seismic excitation is represented by a plane, SH-wave of arbitrary angle 
of incidence. Its displacement component is parallel to the infinite dimension 
of the cavity and, of course, parallel to the free surface. This is schemati- 
cally shown in Figure 37- 

There is a loss in generalization by considering only SH-waves and ignoring 
SV-waves and P-waves. It is justified for this study because it permits the 
easy evaluation of cavity response in a half-space without the complications 
introduced by coupled waves. 

The integral equation method was chosen to evaluate the response of the two- 
dimensional cavity. The integral equation was formulated by the use of the 
appropriate form of the Green's function for the half-space, thereby satisfy- 
ing the stress-free conditions on both the free surface of the half-space and 
on the surface of the cavity. The integral equation was discretized, casting 
it in a matrix form of a system of linear equations with complex coefficients. 



- 105 - 



1 -* 




Figure 37. The cavity, coordinates, and excitation, 



- 106 



The system was solved for impinging plane waves of several angles of inci- 
dence. 

There are basically two approaches to predicting the response of a cavity in a 
half-space: discrete model methods, such as finite difference and finite 
element, and integral equation methods. The advantages and disadvantages of 
the discrete models have been discussed previously (Chapter k) . However, 
it is worth noting that there are several drawbacks to using finite-element 
and finite-difference codes to study cavity response in a half-space. One 
drawback is that a cavity at great depth would require a fine mesh to obtain 
high resolution of the response, thus necessitating a prohibitively large storage 
capacity in the computing machine. Also, radiations from the boundaries of the 
modeled region other than the free surface will contaminate the response. Al- 
though there are special absorbing boundaries to control this effect, the prob- 
lem cannot be entirely eliminated. Another disadvantage of the finite-element 
and finite-difference methods is that a generalized seismic input with an 
arbitrary angle of incidence to the free surface cannot be used. 

The integral equation method offers several unique advantages. Because there 
are no artificial boundaries in the model, spurious reflections do not exist. 
Thus, the radiation of the scattered wave field is correctly incorporated in 
the solution through the use of the Green's function. Furthermore, a cavity at 
great depth does not require a large storage capacity in the computing machine. 
Another advantage of the integral equation method is that through steady-state 
formulation the earth material can readily be made vi scoelastic. Although this 
was not done for this study, it can be easily achieved by the addition of a fre- 
quency-dependent imaginary part to the material modulus. At present, the inte- 
gral equation method has not been developed sufficiently to account for spatial 
variations in material properties. 

Literature Review 

A large number of excellent papers treating the scattering of plane seismic 
waves by cylindrical holes and rigid inclusions have been published; however, 
no studies have been reported on the scattering of seismic waves by cavities in 
a half-space. The scattering of compress ional waves by a rigid cylinder in a 



- 107 - 



full space was studied by Gilbert and Knopoff. 133 They obtained the exact 
solution in integral form, which they evaluated asymptotically for an estimate 
of first motions. Gilbert 131 * presented the scattering of P- , SV- , and SH-waves 
by a cavity of circular cross section in a full space, similarly looking at first 
motions. Banaugh and Goldsmith, 135 using an integral equation formulation, 
studied the scattering of plane steady-state acoustic waves by cavities of 
arbitrary shape embedded in a full space. The transient response of an elas- 
tically lined circular cylinder in a full space excited by a plane compressional 
wave was given by Garnet and Crouzet-Pascal. In a very thorough study, Mow 
and Pao treated both transient and steady-state diffraction problems of all 
wave types by various scattered configurations. Their work also contains an 
excellent bibliographic review of previously published studies. 

Other studies worthy of mention include a very recent paper by Niwa et al., 137 
who used the integral equation method to study the transient stresses around a 
tunnel, lined or unlined. They obtained a good comparison with the results of 
Garnet and Crouzet-Pascal. 136 Niwa et al. 137 also dealt with the full space 
problem, as did all the authors of the previously cited works. Glass 61 sum- 
marized previous closed-form solutions for lined circular cavities and used 
the finite-element method to extend these analyses to adjacent unlined cavities. 
Studies have also been performed by Yoshihara et al. at the University of 
Illinois at Urbana. 138 The above-mentioned publications are not a complete 
bibliographic review, but they serve to highlight the background for this study. 

Theoretical Formulation of Cavity Response 

Consider the displacement field in the half-space as excited by a plane, 
horizontally polarized shear wave of angle of incidence 6 measured between the 
normal to the wave front and the outward normal to the free surface at x 2 = 0. 
The exciting wave is propagating to the left in the positive sense of x\, as 
illustrated in Figure 37- The total displacement in the half-space in the ab- 
sence of the cavity is due to this wave and the reflected wave from the free 
surface. The Fourier transform of this displacement was given by Equation (25): 



U$ {x\ ,x 2 ,oi) = £/o(w) cos (t"^2 cos e )' 



-i -rX\S in6 



- 108 - 



where U®(u) = #3(0, 0,w) , the Fourier transform of the displacement time history 
in the absence of the cavity as observed at point 0. 

The cavity, of radius a, is located with its center at depth xi = D from the 
free surface. Notice that the cavity center is directly beneath point 0. 

Introducing a cylindrical polar coordinate system whose origin is at the cavity 
center, the relation to the original Cartesian system is given by 

Xi = sin t|j (32) 

X2 = D + r cos \\i (33) 

in which the polar angle \p is measured clockwise starting from the a;2 _ axis as 
shown in Figure 38, and r is the polar distance given by 

v - y/ x \ + (jr _ D )2 (34) 

Using these new coordinates, we can alternatively express the incident wave 
field given in Equation (25) as 

.00 . , . „ 
-1 —ps in^s in0 

i/ 3 (r,i|»;w) = tfO(w) cos (j cos 9{D + r cos i|i})e 3 (35) 

Introducing the appropriate form of the Green's function for this problem, it 
is given in the Cartesian coordinates by 

<? 33 ( 3 : 1> x 2 ,5 l ,52.<») - ^•[ ff o 2) (fV( x i • 5i) 2 + («2 " C2) 2 ) 

+ 4 2) (fyfc - si) 2+ <^-?2) 2 )] (36) 

where y is the shear modulus of the half-space, £i and £2 are the coordinates 
of the source point, and 2?J 2 '(Z)is the Hankel function of the second kind of 
order zero of argument Z. Specifically, Equation (36) gives the displacement 
component in the direction 3 at point (xi,x 2 ) due to a line force acting in 
direction 3 at (KitKz) for the harmonic component of frequency to. Notice that 
the second Hankel function in Equation (36) gives the contribution from an image 



- 109 - 







Figure 38. Relation between Cartesian coordinates and 
cylindrical polar coordinates. 



- 110 - 



source representing the effect of the free surface at x<i = 0. Appendix E gives 
the derivation of this Green's function. 

Using the new polar coordinates, we can rewrite the Green's function given in 
Equation (36) as 

^.♦.e...;.) - li [ff(»(| fl ) +ff (2>(|**)] (37) 

in which the source-observation point distance is 

R = / r 2 + t-2 . lrr . cos (^ . n ) (38) 

and the image source-observation point distance is 

R-k = \ r 2 + ^2 + 2rc, cos (ty + n) 

+ kr z (] + £ cos i> + 2| cos n )] 2 (39) 

The coordinates c and ri are the source point cylindrical polar radial distance 
and angle, respectively, analogous to r and ifi of the observation point. 

The problem of determining the response of the cavity surface due to any imping- 
ing wave can be found in the solution to the following integral equation: 65 

U 3 {a,Ti>) = j U 3 {a,ty) 



i 

JA 



VZ(a,n) t- G-Aa^yZ, = a,r\)dA{r\) (40) 



where A denotes the perimeter of the cavity, and n is the outward normal to the 
cavity surface. In Equation (kO) , the frequency w in the function arguments has 
been omitted for convenience. The solution of Equation (40), UAcl,t\), then, is 
the desired displacement response of the cavity perimeter due to the incident 
wave £/ 3 (a,iJ/). Equation (hO) can be discretized as 

N 



+ yaAn ^ ^ a »V ft G 33 {a ^j' a ^\ ] (1|1) 



w=1 

- 111 - 



in which the sum on m replaces the integral, and the incremental circumferential 
length becomes 



dA{r\) = aAn = a jr- 



(42) 



The normal derivative is given by the negative of the radial derivative. This 
last term can be determined from Equation (37) for m £ j as 

y ll G 33 (a '^' a 'V 



l 10 
^ 1 



1 - COS 



— H i 'I— 5— Vl ■ cos ( *7 ~ \ ] ) 



+ H (2) JL 



coa 



1 + cos 



( "V + V + 2 (^ + a C ° S ♦ 



L D 
+ — cos n 

3 a m 



) 



[l + cos bj* % ) +2f cos y|/ 



[* J 1 + cos (f. + X ) + 2g + f cos ^ + £ cos ^)] (43) 

and for m = j after using the appropriate asymptotic form for the Hankel function 
u j£ G 33 (a,$j,a,T\j) 



10) 

5s 



TTwa 1 \ 3 > 



cos 2n - + 2 



(4**f 



cos n 



[l + cos 2n. + 2 £ cos nj -]/ 

[^ V 1+COS2 ^ + 2 (^ +2 - C ° S 3 I 



(MO 



The incident wave expression of Equation (35) can also be evaluated at the same 
discretization points. This yields 



U 3 (aA.) = U° 3 (u) cos f| cos QiD + a cos f.}je 



• CO . , « n 

-i — as i n^ .sine 



(45) 



- 112 - 



Substitution of Equations (43), (44) , and (45) into Equation (41) leads to an 
N x N system of linear equations in lf^(a,tyj) with complex coefficients. 

The response of the cavity lf^ (a ,ip •) , as defined by Equation (41), is put into 
dimensionless form before solution. Dividing it by the Fourier transform of 
the surface motion U% (w) leads to a system of equations in the ratios of the 
cavity response at the discretization points on the circumference to the motion 
above on the free surface. This division conveniently removes the dimension- 
ality of Equation (hi). Thus, the solution has been generalized for any arbi- 
trary time dependence associated with the incident wave. A spectral multi- 
plication of the response ratio for the point on the cavity surface with the 
Fourier transform of the time history to be assigned to the surface motion 
results in the Fourier transform of the response of that point. A Fourier 
inversion yields the corresponding response time history at that point. 

Numerical Study of Cavity Response 

For convenience, the frequency was expressed in a dimensionless form as 

n = <Wb (46) 

and is identical to ft defined by Equation (12). For most applications, the 
dimensionless frequency range 5 ft < 1.0 should be adequate. The significant 
frequencies in damaging earthquakes should range from 0.1 to 15.0 Hz. Shear 
wave velocities should range from 1,000 fps (305 m/sec) for a stiff soil to 
10,000 fps (3,050 m/sec) for granite. For tunnels of radius 10 ft (3 m) , the 
range of interest in the dimensionless frequency would be 0.006 - ft - 0.942 for 
a stiff soil and 0.0006 ^ ft $ 0.094 for granite. Only in the case of a very 
large tunnel -- that is, a tunnel with a radius much greater than 10 ft (3 m) 
— in stiff soils will the range of the dimensionless frequency extend beyond 
1.0. 

The number of discretization points used varied with the frequency of the wave 
motion. For values of ft between zero and 0.4, 16 points were used in the dis- 
cretization. In the interval 0.4 to 0.6, 32 points were used. Finally from 
0.6 to 1.0, 64 points were used. This scheme was selected to assure a suffi- 
cient number of points per wavelength, especially for the higher frequency 



- 113 - 



range. Figure 39 graphically depicts the discretization scheme for N = 8. The 
accuracy of the discretization technique used here was not studied. This con- 
sideration has been reported elsewhere. 65 ' 135 

The solution of the set of equations described above was performed using a com- 
plex Gaussian elimination procedure, which was verified to have an accuracy of 
5 x 10" 13 compared with 1.0. 

Results of Numerical Study . The response ratios obtained in the solution of the 
discretized integral equation are for a particular value of the frequency. As 
an example of the kind of results obtained therein, Figure *f0 shows the response 
ratio values around the circumference of the circle for four different angles 
of incidence of the impinging wave. Both the real and imaginary parts are 
displayed, inward towards the circle center being a positive value. The fre- 
quency for the response depicted in Figure *t0 has the value O.k. The depth- 
to- radius ratio, D/a, is 6. Notice that for 0° angle of incidence the cavity 
response is symmetric about the vertical centerline, as should be expected. As 
the angle of incidence increases to that of a horizontally impinging wave, the 
response becomes more symmetric about the horizontal centerline, although it 
never achieves symmetry because of the influence of the reflected wave from the 
free surface. For the horizontally propagating wave (angle of incidence equal 
to 90°), the real part appears fairly symmetric across the horizontal centerline, 
whereas the zero crossing of the imaginary part is clearly shifted from the 
vertical line passing through the circle's center. Figure *t0 also shows the 
completeness of the solution obtained from the integral equation method used 
in this work. The response of all points around the circumference of the cavity 
is obtained as the system of equations is solved. This is a very desirable 
feature of the method since the response point of interest may depend on the 
particulars of the application. 

Figure *♦! presents the response ratio for the point on the cavity bottom versus 
the dimensionless frequency ft. A single plot was created by repeatedly recon- 
structing the system of equations and solving for a number of different fre- 
quency values to permit a reasonably smooth response curve. Three depth-to 
radius ratios are shown: 6, 20, and 100. These represent a moderate-sized 
tunnel at shallow depth, intermediate depth, and great depth. The results for 



- 11 1» - 




N = 8 

2tt tt 



Figure 39- Discretization scheme for eight points 



- 115 



= O.i) 





Normal 



Wave 
Normal 



£2 = 0.*» 






Real - 
Part 



\\ 



-0.5 


a 


= 6 





=^-- 




magi nary 
\Part 




1 


5 

7^ 




\ \ 

\ \ 





• 5 








r***^ 




Wave 
Normal 



—0.5 



a = o.*» 




Imaginary 
Part 



Figure kO. Effect of angle of incidence on cavity response 
ratio around the circumference. 



116 



Real Part 




Di mens ion less 
Frequency, ->fi 



Imaginary Part 




0.2 0.3 

Dimensionless 
Frequency, ->fi 



a. Shallow depth, D/a = 6 



o 

E — 

° m 

+J CC 
O 

CO <1> 

^r § 

._ Q. 
> </> 

o ce. 



1.2- 



.8- 

.4- 



.V 

.8- 



-1.2- 



Real Part 




Dimensionless 
Frequency, ->fl 



Imaginary Part 



-0.5 



0.2 



0.*i 

Dimens ionless 
Frequency, -HI 




^SgA 



Intermediate depth, D/a = 20 



o 

CD 



CC 




NOTE : Imaginary part for D/a = 100 is 
less than 0.01 for < fi < 0.1. 



Dimensionless 
Frequency, ->Q 

c. Great depth, P/g = 100 

Figure k] . Ratio of steady-state cavity bottom response 

to free-surface response versus frequency for various 

depths and various angles of inclination. 



117 



four angles of incidence, 0°, 30°, 60°, and 90°, are plotted. The range of di- 
mensionless frequency for which the ratios have been displayed is between zero 
and 1.0 for the depth-to-radius ratios of 6 and 20. For the depth-to-radius 
ratio of 100, the dimensionless frequency range is between zero and 0.1. This 
different range in the latter case was chosen because, at the same scale, the 
curves would be very difficult to distinguish due to their many oscillations. 
The behavior of the curves is clearly seen as plotted. The amplitude of the 
imaginary part increases slowly from negligibly small values near zero frequency 
to significant values in the vicinity of ft = 1 . The imaginary part is negligible 
for the range of ft between zero and 0.1. Because the response of the deep cav- 
ity, D/a = 100, is only plotted over that range, the imaginary part was not 
plotted. 

Examination of the diffraction of the SH-wave around the cavity is also of in- 
terest in this study. Thus, a comparison is made between the response at the 
bottom of the cavity and the motion at that same point in the absence of the 
cavity. This undiffracted field is given by Equation (25) in which x = and 
x 2 = D + a. Of course, as in the previous treatment, Equation (25) is first 
normalized by dividing by the quantity Z/2 (w) . This represents both the inci- 
dent plane wave front and the front reflected from the free surface. 

Figure hi gives the comparison between the response of the cavity bottom and 
that of the incident field at the same depth as the cavity bottom (in the ab- 
sence of the cavity) versus the dimensionless frequency ft. Two angles of in- 
cidence, 0° and 60°, are shown for two depth-to-radius ratios of 6 and 20. In 
all cases, at low frequencies the response of the incident field is very close 
to the response of the cavity bottom. The curves slowly diverge as the fre- 
quency increases. Even as the frequency approaches 1.0, the curves of the in- 
cident field are fairly close to those that include scattering. The difference 
shown here between these curves is due to the effect of scattering. It should 
be noted that the imaginary part of the incident field is identically zero. 
Thus, a comparison between it and the imaginary part of the response ratios in 
Figure *tl has not been made. The same comparison for the deep cavity with a 
depth-to-radius ratio of 100 was made; however, these results were not shown on 
this figure because the difference between the incident and scattered fields 
was so slight that they could not be distinguished in a plot. For practical 



- 118 - 




•Cavity Bottom 
Incident Field at Same Depth 
(without cavity) 



a. Shallow depth, D/a = 6 





1 


.2 







8 














.4 


QC 













c 






o 






Q. 
1/1 


-0 


k 


<U 






nr; 








-0 


.8 



1.2- 



Dimensionless 
Frequency, -K2 




Cavi ty Bottom 

Incident Field at Same Depth 
(wi thout cavi ty) 



b. Intermediate depth, D/a = 20 

Figure kl. Motion at cavity bottom and incident 
wave field in absence of cavity. 



- 119 



purposes, it can be concluded that in the frequency range < fi < 0.1 the in- 
cident field and the cavity responses are the same at great depth. 

Other response quantities in this problem that are of interest are the shear 
stresses and strains in the medium around the cavity. These have not explicitly 
been obtained in this study. They can be found by using, for example, a finite- 
difference scheme from the discretized response that has been evaluated. 

Conclusions from Numerical Study . The comparison in Figure k2 suggests that the 
cavity response can be estimated by the incident wave in the low-frequency range. 
How far out on the frequency scale this estimate can be used will depend on the 
acceptable error. The difference between these curves in Figure Ul, then, is a 
measure of error. Scanning the curves and deciding the frequency beyond which 
the difference is unacceptable will define the acceptable low-frequency approxima- 
tion range. Using the incident field will, however, never yield an imaginary part, 

In general, the motion of a shallow cavity in most geologic media will be signif- 
icantly different from the incident wave field (or free-field) motion. For a 
cavity at shallow depth, say D/a = 6, the incident field would provide an ap- 
proximation of the cavity response only for very low frequencies, say < 9, < 
0.1. If the cavity is 10 ft (3 m) or less in radius and located in a competent 
granite, that frequency range is exactly the one of interest. In this case, the 
incident wave field should approximately, but not exactly, represent the cavity 
response. However, in less competent rock or in softer rock with lower wave 
speeds, the frequency range for an earthquake will extend beyond 9, = 0. 1 and 
may even extend to 0, = 1.0. In such rock, the incident wave field will be a 
very poor approximation of the cavity response. This suggests that the seismic 
motion of a shallow cavity strongly interacts with the free surface, particu- 
larly in stiff soils or soft rocks. 

The motion of a cavity at intermediate depth, say D/a = 20, may also be approxi- 
mated by the incident field for very low frequencies. However, at this depth, 
the range < 0, < 0. 1 provides a much better approximation than it affords for 
the shallow cavity, and the range could probably be extended to 0.2 without 
serious consequences. Thus, the seismic motion of an intermediately deep cavity 
also interacts with the free surface, but less strongly than that of a shallow 



- 120 - 



cavity. This interaction is less noticeable for cavities in hard, competent 
rock than for cavities in stiff soil. 

The response of a cavity at great depth, say D/a t 100, is essentially iden- 
tical to the response of the incident field for tne frequency range < 0, < 0. 1 , 
and an excellent approximation is to be expected over a much longer range, say 
< 0, < 0.5- Because low wave velocities corresponding to stiff soils and very 
soft rocks are not, in general, expected at great depths, that frequency range 
should adequately represent most earthquakes. Thus, in general, the seismic 
motion of a deep cavity will not interact or will interact very weakly with the 
free surface so that the cavity response is essentially the same as the incident 
field response at that depth. 

These general statements may be extended to layering of geologic materials. The 
behavior of a cavity near a high- impedance boundary (such as the interface be- 
tween bedrock and an alluvial layer) should be very similar to that of a cavity 
near the free surface. If the cavity is within a distance of 20a from the high- 
impedance surface, significant variations in the cavity behavior with respect to 
the incident field should be expected. Of course, the variations will be greater 
for a cavity located in soft rock than for one located in hard rock. 

This discussion has been in reference to the study undertaken with SH-waves only. 
However, the same general conclusions with respect to proximity of the cavity to 
the free surface and type of geologic medium should apply for P- and SV-waves. 

In summary, the problem of a circular cavity in a half-space subjected to hor- 
izontally polarized shear waves of arbitrary angle of incidence has been studied. 
The steady-state response of the cavity expressed in terms of the free-surface 
motion has been evaluated for a shallow, an intermediate, and a deep cavity. 
Four angles of incidence have been considered for the excitation, giving the 
effect of the full variation of this parameter. Comparisons between the response 
of the cavity and the incident wave field have been presented. These comparisons 
suggest that for low frequencies the diffraction effects are small and cavity 
response can be estimated by the incident, unscattered motion. This applies 
most to deep cavities and hard rock sites. 



- 121 - 



Future research in this field should include examination of damping in the 
earth medium, lining on the cavity, and an arbitrary shape for the cavity 
cross section. Also, the problems of compressional and in-plane shear wave 
excitation of arbitrary angles of incidence, and Rayleigh waves, should be 
investigated. 



- 122 - 



6. Current Practice in Seismic Design 

Seismic design is a part of the overall design process of an underground struc- 
ture, just as it is for a surface structure. The overall design process might 
be schematically represented by the chart in Figure 43. The design process is 
illustrated on the left side of the figure, and the five components of seismic 
design are illustrated on the right side. Construction is included as part of 
the design process because design modifications are usually carried out during 
construction, particularly in the case of excavation within rock. 

It should be noted that the word design has two different meanings. The most 
common meaning refers only to the proportioning of structural components to 
resist the loads without exceeding the failure criteria. This meaning is exem- 
plified by many textbooks in the field of structural engineering whose titles 
refer to the design of steel or reinforced concrete structures. The other mean- 
ing of design refers to the overall process that begins with a statement of need 
for a particular structure and culminates in the detailed specification of the 
structure. In this chapter, seismic design is used in this broader sense and 
includes all those components illustrated on the right side of Figure 43. 

The more narrow sense of seismic design is embodied in the strengthening or 
hardening" of the ground supports. The reader is cautioned not to regard 
strengthening or hardening to mean decreasing flexibility, but instead to mean 
modifying the structure for satisfactory performance under dynamic loads. In 
some circumstances, it might be more appropriate to modify the underground 
structure by increasing rather than decreasing its flexibility because a more 
rigid structure attracts load to it. 

Current practice in the seismic design of underground structures is pri- 
marily defined by papers presented at conferences, by journals, and by design 
criteria documents prepared for specific projects. This literature has been 
reviewed and is summarized in this chapter. Some information has also been 



"Hardening is a term more common to the design of protective structures for 
defense applications. 



- 123 - 



The Design Process 



Seismic Design Components 



Define function to be performed 



Select design concept 



Establish performance criteria 
(based on possible damage modes] 



i 



Seismic performance 
criteria 



I 



Redefine structure if necessary 
to better meet performance 
and failure criteria 





n~£ ; 1 I. 








Ground motion 
characterization 




















r 


Establish engineering 
properties of soil or 
rock 




Dynamic properties 
of soi 1 or rock 






1 


< 










Analyze structural behavior 
(strains and stresses) 




Seismic analysi s 


















r 


Establish failure 
cri teria 




1 


* 1 










Select section properties for 




Seismic strengthening 
(or hardening) 


reinforce 


.men t i f i n 


rock) 







Construction 



Figure 43. The overall design process for underground structures 



- \2h - 



collected through discussions with design engineers of several government 
agencies and engineering firms (see Appendix A). 

Major codes that address the seismic design of surface structures in the United 
States 9 ' 139 " 141 contain no provisions for underground structures. In Japan, 
however, the large number of submerged tunnels constructed since World War II 
have prompted the Japan Society of Civil Engineers to propose a rational seis- 
mic design method titled Specifications for Earthquake Resistant Design of Sub- 
merged Tunnels. 11 * 2 To the best of our knowledge, this is the only example of 
an effort to codify the seismic design of any type of underground structure. 

Earthquake engineering of underground structures addresses the mitigation of 
possible damage from two principal sources: ground shaking and fault rupture. 
Because the design approach to ground shaking is rather dependent upon the type 
of structure and the medium in which the structure is to be built, the discus- 
sion that follows is divided into sections on submerged tunnels, underground 
structures in soil, and underground structures in rock. If an underground 
structure crosses a fault that slips, damage is inevitable, and nothing can be 
done to prevent it; however, certain practices may help reduce the damaging 
effects of fault movement. These practices are described in a separate section 
at the end of the chapter. 

SUBMERGED TUNNELS 

The development of design methodologies for submerged tunnels has been more 
concerned with quantifying the dynamic response of the tube than with selecting 
appropriate properties for the cross section and connections. A description of 
tube behavior requires an understanding of how the ground deforms, how the tube 
conforms to this deformation, the extent of interaction between the structure 
and the soil, and the forces imposed on the structure. There are various 
degrees of sophistication of modeling and assumptions that go into these analy- 
ses. In contrast, the procedures for strengthening (designing in the narrow 
sense) are standard for structural engineering and are governed by codes on the 
design of steel and reinforced concrete structures. 



- 125 - 



In the late 1950s the San Francisco Bay Area Rapid Transit (SFBART) District 
was involved in the design of a subaqueous tube, approximately 3.6 miles 
(5-8 km) long, between San Francisco and Oakland. The tube was to be con- 
structed by placing precast tube segments in a dredged trench, a method that 
had been successfully used for a number of submerged tunnels in the United 
States and Japan, as well as in other countries. However, the seismic environ- 
ment of the Bay Area presented a new design condition that had never before 
been considered for such a structure. No information was available at that 
time on the effects of seismic motion upon subaqueous tunnels, and analytical 
methods for estimating seismic stresses did not yet exist. Consequently, 
SFBART engineers developed their own method for analyzing the tunnel, as pub- 
lished in the Trans-Bay Tube, Technical Supplement to the Engineering Report. 11 * 

The SFBART engineers identified the effects of an earthquake on a submerged 
tube as four different types of behavior: 11 * 

• Curvature deformation in both the horizontal and ver- 
tical planes, imposing bending moments and shear forces 
on the cross section of the tube (Figure kka) 

• Axial deformation, imposing axial forces on the cross 
section of the tube (Figure kka) 

• Dynamic soil pressure, imposing circumferential bending 
moments, radial shear forces, and thrusts in the tube 
wal Is (Figure kkb) 

• Transverse acceleration forces due to the mass of the 
tube, also inducing circumferential bending moments, 
radial shear forces, and thrusts in the tube walls 
(Figure kkb) 

The method developed by SFBART twenty years ago to analyze these four types of 
behavior was based upon readily available solutions in the mechanics of solids 
and the theory of elasticity. The development of the SFBART method predated 
the availability of computer codes for dynamic structural analysis. Today, the 
analytical method of SFBART could be largely replaced by more sophisticated 
computer methods. However, the SFBART procedures are of more than historical 
interest because their conceptualization of tube behavior during an earthquake 
is still at the state of the art. Furthermore, the simplicity of the SFBART 
method makes it very useful today for preliminary design studies. This method 
is summarized below under the heading SFBART Approach to Submerged Tunnels. 



- 126 - 



Due to Curvature 
Deformation in 
the Vertical 
Plane 




Due to Curvature Deformation 
in the Horizontal Plane 



Due to Axial Deformation 



a . Sectional forces due to curvature 
and axial deformations. 




b. Circumferential forces due to dynamic 
soi 1 pressure and inert ial forces. 



Figure kk. Identification of sectional and circumferential forces, 



127 - 



Kuribayashi et al. s0 reviewed the SFBART approach approximately ten years after 
it was developed and proposed some procedural changes, most notably in the spec- 
ification of the ground motion. That work became the basis of the proposed code 
by the Japan Society of Civil Engineers for the design of submerged tunnels. 142 ' 143 
The procedures are summarized under the heading Japanese Approach to Submerged 
Tunnel s. 

The forces developed in a subaqueous tunnel during seismic motion may also be 
investigated by modern computer techniques. These methods are briefly discussed 
and illustrated under the heading Dynamic Analysis of Submerged Tunnels. 

The dynamic behavior of a subaqueous tunnel may be expressed in terms of 
internal forces (or stresses). However, the engineering designer should realize 
that ground shaking imposes a deformation on the structure that is largely un- 
affected by the strength of the structure. Thus, the strengthening of an over- 
stressed section might not result in reduced stresses. It might be more prudent 
under such circumstances to provide sufficient ductility to the structure or to 
articulate the structure by means of seismic joints. In this manner, the struc- 
ture will be able to conform to the seismic deformation without losing its 
capacity to resist static forces. 59 Details of the seismic joint used in the 
SFBART tunnel are described under the heading Special Design Consideration: 
Seismic Joint. 

SFBART Approach to Submerged Tunnels 

Sectional Forces due to Curvature Deformation . Consider first the curvature 
deformation in the horizontal plane, referred to in Reference 14 as transverse- 
horizontal deformation. This deformation can result from the passage of any 
type of plane seismic wave at some oblique angle to the longitudinal axis of 
the tube, although the largest deformations might be caused by a horizontally 
propagating SH-wave. Assume a sinusoidal S-wave with amplitude A and wavelength 
L. The wave geometry is given in Figure 45. This figure represents either an 
SH-wave propagating in a horizontal plane or an SV-wave propagating in the ver- 
tical plane of the tunnel. Propagation along the structure axis, <$> = 0, would 
result in the worst situation. 



- 128 - 








o 




CO 




M- 


._ 


o 


o 




CO 


+J 




c 


M- 


u 


o 


E 




a> 


■M 


u 


c 


fD 


<D 


■ — 


E 


Q. 


<U 


(/) 


o 


•— 


<u 


a 


Q. 


a) 


t/> 


to 




i_ 


Q 


<u 




> 


^_ 


(/> 


<D 


c 




OJ 


X 


l_ 


< 


h- 








c 




c 




3 




•W 




M- 




o 




</> 




X 




ru 




O 




•M 




(U 




3 


^— > 


O" 


-e- 


•— 




w^ 


ifl 


-Q 


O 


O 


o 






0) 


H 




> 


t= 


^ 


<TJ 


CVJ 




2 


% — ■* 






i_ 


c 


fl} 


• — 


<D 


tfl 


-C 




(/) 


-e- 






r— 


w 


OJ 


O 


-o 


o 


•— 




o 


m: 


l/> 




3 


i 


i 


C 



Si 



>• 

i_ 

•M 

<u 

E 
O 



-3- 

0) 

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3 

en 



- 129 



Because the tube is stiffer than the surrounding soil, it will distort less 
than the soil in the absence of the tube, creating zones of tension, compres- 
sion, and shear in the soil around the tube (see Figure kS) . By representing 
the tube and soil interaction as an elastic beam on an elastic foundation and 
neglecting longitudinal shearing stresses between the soil and the tube, we can 
derive expressions for the bending moment and shear force along the tunnel. 
The largest value of the shear would be given by 

v = ^dll A (47) 

and the bending moment by 

M = ^dllll A ( 48) 

1 + {K/E t l){L/2^ 

where: 

K = transverse stiffness modulus of the soil per unit 
length of the tube (in force per unit area) 

E, = modulus of elasticity of the tube 

I = moment of inertia of the tube section 

A = free-field displacement amplitude of a sinusoidal 
S-wave 

L = wavelength of a sinusoidal S-wave 

In the SFBART model, the soil stiffness K is defined as 

K = K.+K + K (kS) 

t o s 

where the subscripts t, c, and s designate tension, compression, and shear, 
respectively. In reality, the tension zone is realized as a reduction in the 
static compression; therefore, K,=K. The compression stiffness K is deter- 
mined by using the Boussinesq theory for a load on an elastic half-space, assum- 
ing that the tube produces a strip load that is alternately positive and nega- 
tive due to the sinusoidal seismic wave. 11 * The expression for K thus deter- 
mined is 

K = E I' - 3 /0.233 (50) 

o s 

where E is the modulus of elasticity of the soil at the level of the tube. 

s 1 



- 130 - 



Ground 
Surface^ 



Tens ion 
Zone 




Free-Field Displacement of Soil 



Displacement of Tube 



Bay Mud 



Compress ion 



Top of Stiff Sublayer 
(or bedrock) 



/ X V 



Figure 46. Interaction between tube and soil due to difference 
between free-field and tube displacements in SFBART approach. 



- 131 - 



The shear stiffness K is determined by assuming that the trapezoidal soil 
prism between the tube and the stiff sublayer resists horizontal deformation 
by uniform shear stresses across the horizontal planes. The geometry of the 
trapezoid is described by the height h of the tube above the bottom of the mud 
layer, the outside diameter d of the tube, and some angle T as defined in 
Figure kj (Reference 14 assumes T = 52.5°). Assuming that the shear modulus 
of the soil varies linearly with depth, the expression for K is 



K 



1G tan T 
o 



In 



where; 



h 



G, (1 + h/h 
t o_ 

Gi 



= d II tan T 
o 



(51) 



G o' G t' G b 



= shear modulus of the soil at a distance x\ 
above the tube, at the level of the tube, 
and at the bottom of the mud layer, respec- 
tively 

h = thickness of soil layer between tube axis 
and stiff sublayer 



Note that, given the width of the tube and an assumed value for T, the value of 

K varies only with the vertical location of the tube within the mud layer. The 

s ' ' 

value of K does not vary with wavelength as do the values of K and K,. 

S G Is 



The design amplitude A is obtained from the ground displacement spectrum, pre- 
pared by Housner. 14 This design spectrum is intended for use in the muds of 
San Francisco Bay, where the shear wave velocity is between 200 and 600 fps (61 
and 183 m/sec) , and for a magnitude 8.2 earthquake on the San Andreas fault. 
The spectrum is represented by a power law 



where: 



A = CL" 

C = k.S x 10" 6 

n = 1 .4 

The units of L and A are in feet. 



(52) 



- 132 - 



Ground Surface 



!\ 




\ 




Assume 
Linear 
Variation 
with Depth 



^-S^h'^'-^'-^'-^'- l *^ Modulus with Dept 



Figure *»7« Assumed geometry for determination of K in SFBART approach. 



Shear 



- 133 - 



The values of L that will maximize the values of shear and bending moment 
within the tube are determined by differentiating Equations (47) and (48) with 
respect to L and setting the results at zero. Since A varies with wavelength, 
Equation (52) is substituted into Equations (47) and (48) prior to differentia- 
tion. Although K also varies with wavelength, it does so gradually and is 
therefore assumed constant. This procedure yields the value of the wavelength, 



L ., which maximizes the shear 
V 



L 



- 2ir 



t n + 1 



K 3 - n 



lA 



(53) 



and the value of the wavelength, L , which maximizes the bending moment 

3 m 3 



L 



m 



= 2ir 



V n + 2 



K 2 - n 



lA 



(54) 



Note that these expressions depend upon the value of K, which, conversely, 
depends upon the wavelength. Consequently, a pair of values for K and L must 
be obtained by the simultaneous solution of Equations (49) and (53) to maximize 
shear and of Equations (49) and (54) to maximize bending moment. 

Next, consider the curvature deformation in the vertical plane, which is re- 
ferred to as transverse-vertical deformation in Reference 14. This deformation 
can also result from the passage of any type of plane wave at some oblique angle 
to the tube; however, the principal effect is probably due to an SV-wave propa- 
gating in the vertical plane of the tube. The maximum values for the shear and 
bending moments within the tube are determined by the same formulas that are used 
for determining the curvature in the horizontal plane, that is, Equations (47) 
and (48), with maximizing wavelengths given by Equations (53) and (54). However, 
some changes in A and K are required, as described below. 

Inspection of recordings of past California earthquakes reveals that vertical 
motions are about one-half to two-thirds as great as horizontal motions. Con- 
sequently, the design amplitude A for vertical motion is computed as two-thirds 
of the value given by Equation (52). 

The soil stiffness modulus, identified for vertical motion as K. cannot be 
determined by Equations (49) through (51). Because rigid vertical geologic 



134 - 



structures do not exist parallel to the tube, significant shear zones are not 
developed on each side of the tube. Furthermore, because the soil above the 
tube is not very thick, no compression (or tension) zone is created in that re- 
gion. Thus K is determined only by the compressive resistance of the soil 
between the tube and the stiff sublayer to a strip loading that is alternately 
positive and negative and that corresponds to the assumed sinusoidal form of the 
seismic wave. Reference 14 utilizes published charts on influence coefficients 
for a soft soil layer over a stiff one to obtain values for K . This procedure 
does not lend itself to a simple representation that could be summarized here. 
For this study, it is sufficient to note that K does vary with L, but not sig- 
nificantly. 

The design values for bending moment and shear force on the tube cross section 
can now be determined for the seismic condition. Maximum bending moments are 
determined separately for horizontal displacement and for vertical displacement, 
as described above. Then the two values are combined by the square-root-of-the- 
sum-of-the-squares method, yielding the design seismic moment. Similarly, the 
design seismic shear is obtained. In a preliminary study assuming a circular 
tube 35 ft (10.7 m) in diameter, buried at a depth of 60 ft ( 1 8. 3 m) in a 100-ft 
(30.5~m) layer of San Francisco Bay mud, Reference 14 computes the design moment 
to be 92,800 kip-ft (125.8 x 10 5 N-m) . The moment of inertia for the prelimi- 
nary concrete configuration of the tube is 37,300 ft 4 (322 m 4 ) . This results in 
a longitudinal seismic stress in the concrete of approximately 300 psi (2.1 MPa) . 

Sectional Forces due to Axial Deformation . Having considered curvature deforma- 
tion, we will now focus on axial deformation. Reference Ik reasons that longi- 
tudinal strains produced in the tube by a P-wave propagating in the direction of 
the tube would be smaller than those produced in the underlying rock. Conse- 
quently, there is no question about the ability of the tube to withstand axial 
strains due to a P-wave. However, a shear wave propagating obliquely to the tube 
can also create axial strain within the tube. As shown in Figure k$, the free- 
field displacement in the soil parallel to the tube axis is 



•) 



u x = isin^ sin (^p-cos \ 



where x is measured along the tunnel axis. Because sin § cos <J> is maximum for 
<j> = ^5°, the worst case for the free-field soil strain parallel to the tube is 

- 135 - 



e = ~ cos \7T L ) (56) 

Reference \k assumes that the tube is more rigid than the soil in the axial 
direction and that therefore the tube restrains the soil in its vicinity from 
experiencing this strain. Thus the axial force created in the tube is equal to 
the force necessary to prevent this strain in the soil. Only the layer of soil 
between the horizontal plane of the tube and the stiff soil sublayer (bedrock) 
is considered. Taking a rectangular block of the soil layer below the tube, the 
force needed to be mobilized over one-quarter of the apparent wavelength {-/iL/h) 
is derived in Reference '\h to be 



F 
a 



- *o S *4¥ + m) <57) 



where G = average shear modulus of the soil, 
av 

Then, assuming that the rest of the soil layer — that is, the soil to each 
side of the tube -- has an effect equal to the rectangular block of soil below 

the tube, the maximum axial force is twice F or 

a 

f = K a a4lT + £h) <58) 

An estimate of the axial force is provided in Reference 1h, assuming a circular 
tube 35 ft (10.7 m) in diameter, buried at a depth of 60 ft ( 1 8. 3 m) in a 100-ft 
(30.5-m) layer of mud in San Francisco Bay. The design wavelength is 500 ft 
(152 m) , following the recommendations of Housner. 14 The design axial force is 
computed to be 7,917 kips (35.22 MN) . Assuming a gross concrete area of 286 ft 2 
(26.6 m 2 ) , this yields a longitudinal seismic stress in the concrete of approx- 
imate 190 psi (1.3 MPa). 

Circumferential Forces due to Dynamic Soil Pressure . So far this discussion of 
the SFBART approach has dealt with the development of bending moments and shear 
forces on the cross section. Now the discussion shifts to circumferential bend- 
ing and the development of circumferential bending moments, radial shear forces, 
and normal thrusts in the wall of the tube by dynamic soil pressure and inertial 
forces of the tube mass. 



- 136 - 



During curvature bending, a pressure develops between the tube and the soil 
because the tube does not displace as much as the free-field soil. This soil 
pressure, derived in the same manner as Equations (47) and (48), is given by 

V = r A (59) 

1 + (K/E t l) (L/2tt) 4 



As discussed earlier, if the curvature is in the horizontal plane, then K = 2K + 

K ; if the curvature is in the vertical plane, K = K . The maximum value of p 
s v r 



is realized for a wavelength 



L = 2tt 
P 



EI_ n 
K ^n 



lA 

(60) 



As an approximate model for circumferential bending, the tube is taken to be a 
circular ring loaded by horizontal and vertical pressure as shown in Figure 48. 
The pressures p, and p. are due to horizontal and vertical displacement, respec- 
tively, and are computed from Equation (59) with appropriate values for K, L, 
and A. From sample calculations in Reference 14, the maximum circumferential 
stress due to dynamic soil pressure is estimated to be about 240 ps i (1.7 MPa) . 

Circumferential Forces due to Inertial Forces . Assuming that the peak horizon- 
tal acceleration of 0.66g, corresponding to the design earthquake, is experi- 
enced by the tube, the horizontal inertial force is O.GGw, where W is the total 
weight of the tube (including roadway) per unit length. As an approximate model 
for circumferential bending, the tube is taken to be a circular ring with the 
inertial force distributed around the circumference and the reactive soil pres- 
sure divided between compression on one side and tension (reduced compression) 
on the other (see Figure 49)- Assuming the weight of the tube to be only 
slightly heavier than the water it displaces and assuming a 35~ft (10.7-m) diam- 
eter and a 2.83-ft (0.86-m) thick wall, the maximum circumferential stress is 
approximately 32 ps i (0.2 MPa). On this basis, circumferential bending due to 
inertial forces may be ignored in more detailed analyses of tube behavior. 

Static-Plus-Seismic Forces . The above discussion summarizes the SFBART approach 
for the determination of stresses induced in the transbay tube by the design 
earthquake. Of course, a subaqueous tube is always designed to resist static 



- 137 - 



p_h 

2 




P_h 
2 



Figure 48. Simple model for the analysis of circumferential 
bending due to dynamic soil pressure in SFBART approach. 



0.66F/ 

2<L 2. 




0.661/ 



J" 2d 



Figure 49. Simple model for the analysis of ci rcumferent ia 
bending due to inertial forces in SFBART approach. 



- 138 - 



stress due to dead load, water pressure, static soil pressure, and temporary 
construction loads. It should be noted that an analysis of permanent static 
load does not predict longitudinal bending; however, a minimum amount of longi- 
tudinal reinforcement is required, even without seismic considerations. Analy- 
sis of the earthquake load did predict longitudinal stresses for the SFBART 
tube, although the values were relatively small. Because standard practice 
(in the United States) permits a 33% increase in the allowable stresses for the 
static-plus-dynamic condition, little additional reinforcement was needed for 
the combined static and earthquake loads on the SFBART tube. 14 ' 

Japanese Approach to Submerged Tunnels 

The Public Works Research Institute (PWRI) of the Ministry of Construction, 
Japan, began research and investigations into the seismic behavior and design 
of submerged tunnels in 19&8. In 1971, the Japan Society of Civil Engineers 
(JSCE) , in close cooperation with the PWRI, organized a committee to establish 
a rational earthquake-resistant design method. The committee's work resulted 
in the 1975 publication of the Specifications for Earthquake Resistant Design 
of Submerged Tunnels. 1 ** 2 Further elaboration of the specifications and a numer- 
ical example are provided by the JSCE document, Earthquake Resistant Design Fea- 
tures of Submerged Tunnels in Japan. 143 Many of the developments in support of 
those two documents, as well as continuing research, are reported in various 
papers and reports by personnel of the PWRI . 60 ' 145 " li+9 

The JSCE specifications cover the complete range of concerns in the design of 
the submerged tunnel. They require site investigations into seismicity, geol- 
ogy, and soil conditions and specify the data to be collected. The procedures 
outlined for seismic design not only cover the precast tubular portion but also 
ventilation towers, approaches, and stability of subsoils. There is even a 
section on the safety equipment and special operating procedures that are needed 
immediately following an earthquake. In the summary below, the emphasis is 
placed on the submerged tube." 



>A1 though the major emphasis will be on the precast tube portion of the sub- 
aqueous tunnel, other portions also should be investigated, including the ven- 
tilation towers, the approaches, and the soil fills. The Japanese specifica- 
tions provide a very detailed checklist of all the various considerations for 
design. l42 , 143 

- 139 - 



Sectional Forces due to Axial and Curvature Deformation . In the Japanese 
approach, the sectional forces (bending moment, shear and axial forces) are 
determined by the seismic deformation method, which closely parallels the SFBART 
approach for curvature bending. The method is derived by assuming that a shear 
wave propagates with an angle <\> to the axis of the tunnel (see Figure 45). 

The shear force and bending moment are derived with the same assumptions as the 
SFBART approach (wave propagating along axis, <j> = 0, and elastic beam on an elas- 
tic foundation). The resulting formulas are identical in form to Equations (47) 
and (48): 

K L/2v 
V = -A (61) 

1 + (K 2 /E t l)(L/2^)^ 

K (L/2*) 2 

M = - A (62) 

1 + (K 2 /E t l)(L/2^)^ 

The previous designation for the soil stiffness in these two equations has been 
changed from K to K^ because the Japanese use a different technique to determine 
soil stiffness. 

The free-field displacement parallel to the tunnel axis, given by Equation (55), 
induces an apparent axial strain in the tunnel. This strain is maximized by <f> = 
45°, as in Equation (56). The SFBART approach assumes that the tube is rigid; 
the Japanese approach, however, assumes that the tube is an elastic rod embedded 
in an elastic foundation. Consequently, part of the free-field displacement 
creates a force in the tube, while the remainder creates an equilibrating force 
in the surrounding soil. Following these concepts and selecting the appropriate 
value for x, the largest value for the axial force is 

Z,L/2ir 

P = 1 -A (63) 

1 + (K/E.A )(v / 2L/2tt) 2 

1 u G 



where: 



K x = longitudinal stiffness modulus of the soil per unit 
length of the tube 

A = cross-sectional area of the tube 
a 



- 140 - 



K\ and K 2 are estimated by considering the tunnel to be a rigid rectangular 
plate on the semi- inf ini te elastic body so that 



l 2 av 



(6k) 



where G is the average shear modulus of the soil. This is in contrast to the 
av 3 

SFBART procedures for obtaining the soil stiffness represented by Equations (kS) , 
(50), and (51). 



The values of wavelength L that will maximize Equations (6l), (62), and (63) 
are determined by differentiating with respect to L and setting the results equal 
to zero. The fact that the wave amplitude varies with L is ignored in the Japa- 
nese approach so that the maximizing wavelengths can be obtained. The wave- 
lengths for maximum values of shear force, bending moment, and axial force are, 
respect ively, 

lA 

(65) 



m 



= 2tt 



= 2-ir 



V 



3#2 



V 



K 2 



lA 



(66) 



= 2tt 



E.A 

t c 



2Zi 



(67) 



Substituting Equations (65), (66), and (67) into Equations (61), (62), and (63), 
respectively, yields the design sectional forces 



V 



max 



M 



max 



ir*^7v A 



jSk^Ja 



(68) 
(69) 



/2 



P - -tt VKTe^A A 

max H 1 t Q 



(70) 



The design value for the ground displacement, A, is determined by using a 
response spectrum that is similar, but not identical, to that of the SFBART 



- 141 - 



approach. The horizontal ground displacement amplitude at the ground surface 
is obtained by the formula 

A = 2- 5, • T • a, • f T (71) 



Tf2 v br J I 



where: 



S = relative response velocity per Gal of the maximum 
acceleration at the bedrock (1 Gal = 1 cm/sec 2 = 
0.001g) 

T = fundamental natural period of the subsurface layer 

a-i = horizontal acceleration at the bedrock in Gal 

f = importance factor 

When the vertical displacement amplitude is needed, it is to be one-quarter to 
one-half of the horizontal values according to the Japanese specifications. 

The relative response velocity can be obtained from the spectral curves shown 
in Figure 50, which were developed by the PWRI from seismic records measured on 
bedrock in Japan. Similar spectral curves were developed by the Port and Harbor 
Research Institute, Ministry of Transportation. The natural period of the soil 
layer may be obtained either by observation of microseismisms or from the formula 

T = y- (72) 

s 

where H is the thickness of the layer and V is the shear wave velocity. The 
importance factor f T is 1.0 for "tunnels serving higher public interests" and 
0.8 for all other situations. Finally, the horizontal acceleration at the bed- 
rock surface is stipulated as 

%r = 4 ' a (73) 

where: 

f = seismic zone factor, equal to 1.0, 0.85, and 0.70, 
depending upon the location in Japan 

a Q = standard horizontal acceleration at bedrock surface 
in Japan, taken as 100 to 150 Gal (0.102g to 0.1 53g) 

The above procedures, which the Japanese refer to as the seismic deformation 
method, provide a rational approach to the computation of sectional forces along 

- 142 - 



D 




CL 




c 








4-> 


p— 


. — 


fO 


c 


o 


Z3 


*v» 




o 


l_ 


<u 


<D 


If) 


Q_ "v 




E 


>- 


o 


4-1 


* — ' 


O 


£> 


o 


CO 


0) 


. 


> 


c 




o 


0) 


•— 


10 


4-1 


c 


fD 


o 


l_ 


Q. 


a> 


i/> 


■_ 


0) 


<u 


cc 


o 




o 


<u 


< 


> 




• — 


c 


4-1 


o 


OJ 


•— 


■— 


4-J 


0) 


o 


q; 


2: 



0.30 

0.20 
0.15 

0.10 
0.08 

0.05- 



0.02 



0.1 



f 


Damping Ratio 0.00 


: 


^* 0.02 


i 




/ 


/ 0.05 




/ A 


r x . 1 


/ / 




/ / / 


^"^ 0.20 


/ I / / 




. > 


0.40 
— 1 1 1 — 1 — 1 — III,- -1— 1 1— -J 



0.2 0.5 0.7 1.0 2.0 
Natural Period, T (sec) 



5-0 



Note : 1 cm/sec/Gal = 386 in./sec/g. 



Figure 50. Relative response velocity per unit acceleration 
(Adapted from Reference 1*5.) 



1*3 



a submerged tunnel. This approach could be used In the design of a subaqueous 
tunnel project for any seismic region in the world, requiring only an appropri- 
ate site-dependent determination of S and au . 

Soil pressures during earthquakes are considered in the Japanese approach as 
they are in the SFBART approach; however, the methods for obtaining them differ. 
The Japanese specifications require that the horizontal earth pressures be 
determined by the Mononobe-Okabe earth pressure formula. A discussion of the 
Mononobe-Okabe approach is provided by Seed and Whitman. 150 The Mononobe-Okabe 
formula is presented later in this chapter in the section on tunnels in soil. 

Circumferential Forces due to Dynamic Soil Pressure and Inertial Forces . The 
Japanese specifications also require the application of the seismic coefficient 
method to the design of the transverse section and the examination for sliding 
of the tunnel. In this method inertial forces arising from the weight of the 
structure itself, its contents, and the surrounding soil fill are applied as 
static equivalent forces. The horizontal seismic design coefficient k-, in Japan 
is to be obtained by the following formula: 

K = f'fr'f,' Kt* (74) 



where: 



"h J z J I J s oh 



f = seismic zone factor, as defined for Equation (73) 

f = importance factor, as defined for Equation (71) 

f = ground condition factor, ranging from 0.9 for bed- 
rock to 1.2 for very poor soil conditions 

k ■, = 0.2, standard seismic design coefficient 



The vertical seismic design coefficient k is stipulated to be one-half of k-, . 
Both the SFBART and the Japanese approaches investigate circumferential bending 
of the transverse section; however, the SFBART approach is not concerned with 
sliding of the tunnel in the soft soils. A major difference between the two 
approaches is in the horizontal seismic coefficient: 0.66 for the SFBART pro- 
cedure and approximately 0.20 for the Japanese procedure. 



- ]kk - 



Dynamic Analysis of Submerged Tunnels 

The bending moments and forces created in a submerged tunnel by an earthquake 
can also be determined by using the computer methods described in Chapter k. 
Computer models permit more accurate descriptions of the physical systems and 
the input motions than do the seismic deformation and coefficient methods. 
However, this does not necessarily mean that the computer models should replace 
the seismic deformation and coefficient methods. In fact, the Japanese speci- 
fications 142 require both: 

Any part of the structural system shall be designed by the 
seismic deformation method and the seismic coefficient 
method. . . .Also the total structural system shall be 
designed according to the results of the dynamic response 
analysis, in which the influence of the surrounding topog- 
raphy and geology on the tunnel shall be considered. 

An appropriate model for the determination of sectional forces uses beam ele- 
ments to represent the tunnel segments and a lumped -parameter system to repre- 
sent the soil. 95 ' 96 The input motion for this model is represented either by a 
response spectrum or by a time history at the bedrock. Kuribayashi et al . 
present the results of a computer model analysis of the proposed highway tunnel 
crossing Tokyo Bay between Kawasaki and Kisaraza. 60 ' 11+5 In Figure 51, the 
results of this analysis (which uses an averaged response spectrum with a maxi- 
mum acceleration of 150 Gal) are compared with the results of the seismic defor- 
mation analysis. The model is also analyzed for four earthquake time histories; 
the results are shown in Figure 52, with the peak accelerations given in paren- 
theses after the name of each earthquake. 

Circumferential bending due to seismic earth pressures and inertial forces can 
be investigated by a two-dimensional finite-element model of the tube cross sec- 
tion and a portion of the surrounding soil. If sufficient details of the con- 
crete cross section and circumferential reinforcement are modeled in the finite- 
element scheme, the details in the cracking of the concrete can be readily 
studied. 146 

Japanese investigators have also studied other aspects of dynamic analysis of 
submerged structures. For example, the literature includes references to re- 
sponse spectra, 151 motion recorded in submerged tunnels, 95 ' 96 ' 152 and physical 
models. 95 ' 96 ' 153 

- 1i»5 - 



Length of Submerged Tunnel 3,340 





(tm) 
500,000- 

400,000 

300,000 

200,000 

100,000 





- 






(a) 


Axial Force- (t ) 


- 


/A 

1 \ 


'""■"s^'* 




// \ 


A 


^_„'-\ ^,s\ / \\ 










V --"^-"-"" / \ 



lb) Bending Moment (tm) 




( c ) Shearing Force ( t ) 



Seismic Deformation Analysis 

Dynamic Analysis using Average 
Response Spectrum (150 Gal) 



NOTE : 1 m = 3-28 ft; 1 t = 2,205 lb; 

1 tm = 7,233 ft-lb; 1 Gal = O.OOlg. 



Figure 51. Distribution of sectional forces by seismic 

deformation analysis and dynamic analysis. 

(Source: Reference 1^5.) 



- \kS 



Tunnel Length - 3.340 m 




H m m m u 



(c) Shearing Force (t) 

Off Nemuro Peninsula Earthquake (k5 Gal) 
Hachijyo Island Earthquake (10 Gal) 
Off Echizen Cape Earthquake (22 Gal) 
Tama River Earthquake (6 Gal) 



NOTE : 1 m = 3.28 ft; 1 t = 2,205 lb; 

1 tm = 7,233 ft-lb; 1 Gal = 0.001g. 



Figure 52. Distribution of sectional forces by dynamic 
analysis using four different earthquake waves. 
(Source: Reference 145.) 



147 - 



Special Design Consideration: Seismic Joint 

An important design consideration for submerged tunnels is the possibility of 
differential motion between the ends of the tube and its approaches. In gen- 
eral, a tube lies in the soft muds below the waterway, while the tunnel 
approaches pass through firmer soil. During earthquake vibrations the two soil 
masses will respond differently, producing differential displacements between 
the precast tube and the tunnel approaches. 

The San Francisco approach of the SFBART transbay tube consists of two shield- 
driven, steel-ring tunnels with a transition to the tube at a ventilation struc- 
ture founded 400 ft (122 m) offshore in the San Francisco Bay mud. The Oakland 
approach, a cut-and-cover tunnel, is connected to the tube by an onshore venti- 
lation structure. The transbay tube itself, consisting of 57 prefabricated 
tube segments placed in a dredged trench, spans a distance of approximately 
3.6 miles (5.6 km) between ventilation structures. 

Theoretical analyses and tests of scale models indicated that there would be 
differential movements between the SFBART tube and the ventilation structures 
during ground shaking. Thus, a seismic joint was incorporated into the tube 
segments at each end to permit calculated movements during an earthquake of 
1-1/2 in. (3.8 cm) in either direction axial to the tube and k in. (10.2 cm) in 
any direction transverse to the tube (i.e., in the vertical plane between the 
tube and the ventilation building). An additional 2 in. (5.1 cm) was permitted 
in the vertical plane to allow for the possibility of differential settlement. 
A sliding joint was devised to accommodate these movements as well as the earth 
and water pressure. 

The details of the sliding joint are illustrated in Figure 53. The joint con- 
sists of six major elements, as described below by Douglas and Warshaw: 54 

1. Bracket - The bracket is rigidly attached to the tunnel 
section, and around the periphery of the bracket are 
two elastic gaskets that act in a manner very similar 
to a piston ring. 

2. Collar - The collar is a ring section that is designed 
to slip over the gaskets of the bracket in a manner 
similar to a cylinder of an automobile over a piston. 
The inside face of the collar is designed to permit it 



- 148 - 



BOOT 
FIXED RING 



EXTERIOR 
FACE OF 
TUBE 



* / 




GASKETS- 



WIRE ROPE ASSEMBLY 



-TEFLONH 

BRACKET 



Inside face of tube 

Reprinted by permission of the publisher. 



COLLAR 

-A/VIRE ROPE 



-BOOT 

EXTERIOR FACE 
' OF TUBE 




Inside face of tube 



Figure 53. Details of seismic joint for the SFBART subaqueous tube, 

(Source: Reference 15^.) 



1^9 



to slide along the bracket gaskets. The dimensions of 
the sliding surface are such that when the collar is 
placed over the bracket the collar will compress the 
bracket gaskets to form a watertight seal. Two elastic 
gaskets are placed on the vertical face of the collar. 

3- Fixed Ring - The fixed ring is a tunnel-shaped section 
rigidly attached to the building. When the collar is 
assembled to the fixed ring these gaskets are compressed 
on the vertical face of the fixed ring in such a way 
that they provide a watertight seal. The vertical face 
of the fixed ring is designed to permit gaskets on the 
collar to slide along this face. 

k. Wire Ropes - In order to compress the collar gaskets 
to the face of the fixed ring, wire ropes are placed 
between the collar and the fixed ring and tensioned, 
thereby compressing the gaskets. The wire ropes are 
flexible and are designed so that they can safely carry 
the increased stress in them because of the sliding 
movement of the joint. Wire ropes are also used to 
compress the bracket gaskets to the collar as well as 
to transmit any unbalanced loads on the collar to the 
bracket. 

5. Gaskets - These elements are made of a rubber compound 
and are attached to the collar and the bracket and pro- 
vide the watertight seal between components. 

6. Teflon Surfaces - In order for the sliding joint to be 
effective, it has to be able to move under a small 
force which will not damage the tunnels or the build- 
ings. The only restraint to the motions in the sliding 
joint is the frictional force which will develop be- 
tween the gaskets and the faces on which they are in 
contact. The coefficient of friction between rubber 

on steel is high and, if the rubber gaskets were di- 
rectly in contact with steel, the force to overcome the 
friction of the rubber against the steel face would be 
such that the stresses produced in the tunnel and 
building would be too high. Therefore, all surfaces in 
contact with the rubber gaskets were faced with Teflon 
in order to reduce the restraining frictional force to 
a value that will minimize the stresses in the struc- 
tures . 



UNDERGROUND STRUCTURES IN SOIL 

Most underground structures in soil are tunnels for the conveyance of motor 
vehicles, trains, fresh water, or wastewater. Such structures are distinguished 
by being very long compared with their cross-sectional dimensions because their 
purpose is to connect places together, not to provide volume. Other underground 

- 150 - 



structures, such as convention halls, parking garages, office areas, or water 
reservoirs, provide volume or enclose spaces. (The basement portion of surface 
structures is not included in this definition of underground structures.) Seis- 
mic design concerns for tunnels and for volume structures in soil are similar. 
However, the specific procedures and formulas for curvature and axial deforma- 
tions presented below are developed for tunnels and are not directly applicable 
to volume structures. 

SFBART Approach to Structures in Soil 

The method of analysis for curvature and axial deformation of a lined tunnel 
in soil is similar to that for a subaqueous tube. Assuming an elastic beam 
embedded in an elastic medium, the formulas for sectional forces would be Equa- 
tions (61), (62) , and (63) . 

Kuesel, in setting forth the seismic design criteria used for the SFBART sub- 
ways, describes a departure from that approach. 59 Instead of assuming inter- 
action between the soil and the structure, Kuesel makes the more conservative 
assumption that the structure conforms to the shear wave deformation shown in 
Figure k$. The strain due to axial displacements is 



9w . . 

x 2i\A 

a dx L 



sin <j> cos <j> cos [— x cos $\ (75) 



From the theory of bending for an elastic beam, the extreme fiber strain is 

s, = 5& (76) 



where: 



'b R 



B = width of the tunnel structure in the plane of bending 
R = radius of curvature of bending 



The radius of curvature is derived by 

d 2 u 



1 



#„ ft 2 

° d X 



3 % fay. 3 A . /2u \ ,,_. 

2- = -I --I A cos 5 $ sinl-jp— x cos <j>l (77) 



- 153 - 



Neglecting the fact that Equations (75) and (77) are maximized by different 
values of x, Kuesel gives the combined axial and bending strain as 

e = j- 2 sin (J> cos <j> + —- cos 3 J (78) 

Clearly this is maximized by minimizing the value of L. Because Equation (76) 
is valid as long as the beam-span-to-depth ratio does not become much less than 
3, 155 Kuesel assumes L/cos <J> = 65. Substituting this assumption into Equation 
(78) yields 



= — 2 sin $ cos <j) + ~- cos 2 <)> 



(79) 



The function in brackets has a maximum value of 1.67 for § = 32°; therefore, 

■nA ~ r n A 



G 



= 1.67 f^ = 5.2 f (80) 



max L L 



in which L is taken as 65 (this should be SB cos 32°, but cos 32° is dropped for 
convenience). The value of A i s determined from Equation (52), the design dis- 
placement spectrum for SFBART, as 

A = CL n 

where C = 1.0 x 10~ 7 for loose sand and soft clay or 1.1 x 10~ 8 for dense sand 
and stiff clay and where n = 1.86 for loose sand and soft clay or 1.95 for dense 
sand and stiff clay. The units of A and L are in feet. 

Box structures in soils are subject to racking by shear distortions in the soil, 
as illustrated in Figure 5^. The amount of racking r imposed on the structure 
is estimated from the assumed distortions in the soil. Assuming T = u /h (see 

y 

Figure 5*0, Kuesel uses a parametric study to determine an approximate relation 
for the racking in terms of the depth of the soil layer and the shear wave 
velocity of the soil. Because that approximate relation is only applicable to 
the soil conditions in the locations of the SFBART subway structures, it is not 
presented here. Regardless of how the shear distortion is determined, the capac- 
ity of the reinforced concrete box structure to withstand the racking within 
accepted limits of elastic and plastic distortion must be investigated. When 
the imposed shear distortion creates plastic rotation of joints, such joints 
should be detailed in accordance with design practice for reinforced concrete 
structures. 

- 152 - 



Displacements in Soil 
Relative to Bedrock 



ry 



Soil 
Mass 



Bedrock 



r~* 1 I 1 / 

/ / 

/ / 

; / 

( ' 



■*^p> **^W~ 




Figure $k. Racking due to shear distortion of the soil 



153 



Mononobe-Okabe Theory of Dynamic Soil Pressure 

Lateral earth pressures on earth-retaining structures increase during earth- 
quakes. Although most codes do not recognize this fact, 9 ' 139 " 141 the need to 
consider increases in the lateral earth pressure on underground structures is 
recognized in several documents, namely the Japanese Specification for Earth- 
quake Resistant Design of Submerged Tunnels,^ 2 the SFBART procedures, 14 and 
the seismic design requirements of the East Bay Municipal Utility District. 156 
The accepted theory for determining the increase in lateral earth pressure is 
the Mononobe-Okabe theory, which is described by Seed and Whitman. 150 



Using the Coulomb theory, Mononobe and Okabe compute the active earth pressure 



P.„ during an earthquake to be 150 
AE 



AE 



- KV<'-V 



K 



AE 



(81) 



where 



K 



AE 



COS' 



(#-§-¥) 



w 



COS § COS' 



V , cos (6 + ¥ + §) S 2 
WW 



H 



w 



w 



V 



= tan 



-1 



1 - k 



5 = 1 + 



sin ($ + 6) sin (* - § - V ) 



cos (6 + 5 + §) cos (¥ - ¥ ) 
w g w 



1/2 



= unit weight of soi 1 

= height of retaining wall 

= angle of friction of soil 

= angle of wall friction 

= slope of ground surface behind wall 

= slope of back of wall to vertical 

= horizontal design ground acceleration (in g) 

= vertical design ground acceleration (in g) 



Seed proposes that the increment of dynamic pressure AP.„ above the static pres- 
sure can be approximated by 150 



2 s w H h 



*P AE = TY-tf- 2 ■** 



(82) 



- 154 - 



For the underground box structure with shallow cover, H is the vertical 

w 

dimension of the structure. Mononobe and Okabe considered that the total 

pressure computed by Equation (8l) would act on the wall at the height of H /3 

w 

above the base. However, in the underground structure, vertical walls are re- 
strained at the top as well as at the bottom. Consequently, it is more appro- 
priate to apply the additional seismic earth pressure at midheight, so as 
to distribute it uniformly over the depth of the structure. 

It should be noted that the static-plus-seismic earth pressure will usually 
not create a more severe design situation than the static-only earth pressure. 
During dynamic loading, allowable stresses may be increased by one-third. 
A study of the seismic earth pressure, Equation (82), reveals that the static 
design can probably withstand accelerations up to about 0.2g or 0.25g. 150 

Computer Methods for Structures in Soil 

Structures in soil can be analyzed using modern computer techniques much as 
subaqueous tunnels can. For example, a two-dimensional finite-element model, 
subjected to an input seismic motion, can be used to calculate stresses in the 
walls of the structure. Sectional forces can be evaluated using computer 
models of elastic beams for the structure and lumped masses and springs for 
the surrounding soil. 

Two-dimensional computer models of cross sections of long tunnels are neither 
practical nor necessary along the entire length of the tunnel. Such models are 
impractical because they would require a prohibitively expensive exploration 
program to determine soil properties along the entire length. The dynamic be- 
havior can be adequately evaluated by modeling several sections that bound the 
extremes of the problem. When the structure serves a critical function, more 
extensive computer modeling may be required. If the linear extent of the crit- 
ical structure is confined, then an extensive exploration program to support 
the modeling effort will not be as costly as it would be for a long tunnel. 
Examples of critical structures for which more extensive modeling may be both 
necessary and practical are water reservoirs and subaqueous tunnel approaches. 



- 155 - 



Special Considerations In Design 

Rock Intrusions . Rock zones within a soil mass may provide a hard bearing point 
for the underground structure during seismic activity. At transitions from soil 
to rock and at locations where bedrock juts into the excavation region, the 
structure should not be cast directly against the rock. Kuesel suggests at 
least a 2-ft (0.6-m) over-excavation filled with soil or aggregate backfill. 59 

Abrupt Changes in Cross Section . Discontinuities in the underground structure 
itself may also present problems. The designers of SFBART recognized that the 
junction of a tunnel structure with a larger station structure will be sub- 
jected to differential rotation and translation due to the difference in stiff- 
nesses of the two structures. It is better to design the joints at these 
junctions to accommodate the differential deformations than to provide rigid 
connections. 5 This principle should be followed wherever abrupt changes in 
the underground structure occur. 

Corner Reinforcement . In the static design of a box-type cut-and-eover structure, 
the vertical reinforcing steel on the inside face of the earth-retaining walls 
is only needed in the midheight regions of the walls. To simplify placement 
of reinforcement, this steel is usually extended to the top and the bottom of 
the wall. However, during racking, the inside face of the corners will ex- 
perience tension. Therefore, for seismic considerations, the steel should be 
further extended into the top and bottom slabs and hooked at the far face, as 
illustrated in Figure 55. This detail was included in the design of the rein- 

157 

forced concrete tunnel structure of the Stanford Linear Accelerator. 

Abrupt Soil-Rock Interface . If a tunnel must be excavated through an abrupt 
interface between large soil and rock masses, a seismic joint may be required. 
For example, the North Point tunnel (North Shore Outfalls Consolidation, 
Contract N-2) of the current construction program in the San Francisco Waste- 
water System will pass through an abrupt soil-rock interface. An evaluation 
of the relative motion between the tunnel in rock and the tunnel in soil was 
conducted by Dames S Moore, one of the geotechnical consultants to the waste- 
water program. They recommended design for a relative tunnel displacement of 
12 in. (30.5 cm) in any direction over a distance of approximately 50 ft 



- 156 - 




Soil 



Figure 55. Corner details for seismic design, 



157 - 



(15.2 m) where the tunnel passes abruptly from rock to soft soil. 158 Thus the 
wastewater program has specified the construction of a seismic joint at the 
rock-soil interface and another seismic joint 50 ft (15.2 m) from the interface 
in the soil. 159 Details of the seismic joint are illustrated in Figure 56, 
which is based upon construction drawings. 160 The 1-in. (2.5^-cm) thickness 
of crushable styrofoam in the joint will allow the joint to articulate suffi- 
ciently to conform to the predicted displacements. This detail would be very 
difficult to construct in a tunneling operation, especially if wet, running soils 
are encountered. However, the detail is feasible for cut-and-cover construction. 

Excess Pore Pressure . Excess pore pressure due to seismic motion may create 
a potential for uplift on a box structure; one possible solution to this prob- 
lem has been adopted for the San Francisco Wastewater System. The large sewer 
box structure under Marina Boulevard (North Shore Outfalls Consolidation, 
Contract N-*t) will pass through soil with a high potential for liquefaction 
during an earthquake. One possible consequence of liquefaction is uplift of 
the box structure due to excess pore pressure acting on the* underside of the 
structure. To mitigate this effect, Dames & Moore recommended gravel drains 
beneath the structure and gravel drains along the sides extending above the 
water table. This will permit excess pore pressure to dissipate, thereby 
reducing uplift. The bottom drain must be continuous, which can be easily 
achieved by over-excavation and backfilling with gravel. Because longitudinally 
continuous side drains introduce construction difficulties, vertical gravel 
drains can be developed by using alternate cells of steel sheet piling. Details 
of the gravel drains are illustrated in Figures 57 and 58, which are based upon 
construction drawings. 160 

UNDERGROUND STRUCTURES IN ROCK 

The distinction between the supports for tunnels in rock and those in soil may 
be blurred because of the large range of conditions that exists in both rock 
and soil. However, openings in competent rock are often quite different from 
those in soil. Competent rock in general permits larger spans and may require 
little or no support for static stabilization. If support is needed, it may 
consist of rock bolts and/or a thin layer of shotcrete. When considering the 
dynamic behavior of such underground structures, it is readily apparent that the 
lining, if it exists, is so flexible that it cannot be thought of as an elastic 

- 158 - 



f 



m 



j- 



A 



r 






N 



■V 



/ 



9'-0" 



Approved Sealant 
(all around) 



Approved Neoprene Ring 

(tightly fitted continuously 

around tunnel lining)- 

Crushable Styrofoam 

(glued al 1 around) 
Tunnel Lining 




2'-0" Collar 



13 #8 Hoops as Shown 



#6 @ 8 



NOTE: 1 in. = 2.5^ cm; 1 ft = 0.30^8 



Figure 56. Seismic joint for North Point tunnel 
(Adapted from Reference 160.) 



- 159 



JMUW. VI 



Ground Surface 



IT 



YWV////VW 



Symmetrical 



^^ Sheet 
■'■'9Co'T Minim 




11-1/2" 



Pile 11-1/2" 
mum Depth 



6" Minimum!' 



Crush Rock Fi 1 1 

Drain Rock Layer 
Fi 1 ter Rock Layer 



NOTE: 1 in. = 2. 5*4 cm; 1 ft = 0.30^8 m. 



Figure 57. Cross-sectional details of drain for Marina 
Boulevard box. (Adapted from Reference 160.) 



- 160 - 



11-1/2'^ 
Minimum 



Concrete Wal 1 



I' . ■ -J '■■ ' ■ ' ,-..•'■■ ' ' ' ■ !' ■ •■ ' . 1 . \.f l > ' I t .. ' ""■ . '■ ' . ' -■ ■»■■ ■ ' ' ■ ■* ! -•■■ ■■ ' ! 

f.-.---'' , ':-:>' ,r -'--j|r" h '-.'-- , v : "'''-* "■- * -VA'*'/-. :r .= ',"-';.*?. °. ;■■"• •/..'*■•■*■■-:'. 



Drain Rock 




38 



Sheet Piles* are Selected by 
Contractor and May be Removed 
after Completion. 



Section A-A 



NOTE: 1 in. = 2.54 cm. 



"If sheet piling is not used, equivalent 
vertical drain passage shall be provided 
with the approval of the engineer. Con- 
tinuity between vertical drains and bot- 
tom drain rock layer must be provided. 



Figure 58. Detail of vertical drain for Marina Boulevard box, 
(Adapted from Reference 160.) 



- 161 - 



beam embedded in an elastic medium as is the case for many structures in soil. 
Steel sets with lagging, often used in poor rock, also cannot be viewed in this 
way. Reinforced shotcrete liners for poor rock or the thick concrete liner often 
required in highway tunnels or water conveyances (for reasons other than static 
stability) may be considered embedded beams, although the moduli of the liner 
material and the rock are approximately the same. Consequently, many of the 
simplifying assumptions employed in modeling the dynamic behavior of structures 
in soil cannot be used for structures in rock. For this reason, and because of 
the popular assumption that openings in rock are not vulnerable to earthquake 
motion, the current practice of earthquake engineering is poorly developed for 
structures in rock. 

Perhaps another reason for this retarded development is that the static design 
in rock is largely dominated by empirical procedures. The development of 
sophisticated dynamic design methods is not encouraged because of the lack of 
compatibility with prevalent static design methods. However, this situation 
may be changing. In recent years there have been many studies evaluating static 
ground-liner interaction and design procedures. 162 " 167 It may be that these 
activities will lead to significant gains in the state of the art within static 
design. Thus, at this time, very little can be discussed about seismic design 
procedures other than to point out what has been tried to date and some of the 
potential developments. 

Design Based on Geologic Engineering Principles 

A simple approach to earthquake engineering of rock tunnels was developed 
and applied to a conceptual design study of a proposed nuclear waste reposi- 
tory. 63 ' 168 With this approach, dynamic stresses are calculated using a sim- 
plified model for determining free-field stresses within the rock mass and 
assuming a plane compressive or shear wave propagating in a homogeneous f u 11- 
space. This method is explained in Chapter k and is based upon Equations (6) 
and (10): 

a = ±pV \V , | 
max p\ peak J 

T = ±pV \V , I 

max K s\ n, peak I 

The approach ignores the nonhomogenei ties and discontinuities in the rock, 
the refraction of wave energy around the opening, and the complicated 

- 162 - 



superposition of incident and reflective waves from the free ground surface. 
However, such computations seem to be acceptable within the largely empirical 
framework of current underground static design. Dynamic stresses determined 
by this procedure are compared with the estimated in situ stresses. If the 
subtraction of a tensile seismic stress pulse from the compressive in situ 
stresses results in tensile stresses in the rock, seams may open and permit 
rock blocks in the tunnel to loosen (and perhaps even to fall) as the tensile 
pulse passes. Thus, an approximate evaluation of the dynamic stability of a 
tunnel is provided. 

In addition to a rough determination of seismic stresses, Reference 1 68 sug- 
gests a further evaluation of the dynamic response of the cavity by reviewing 
the reported experience from tunnels exposed to dynamic loads and by quali- 
tatively considering the interaction between supports and surrounding rock. 
Two very different stabilization systems are considered, one using steel sets, 
as shown in Figure 59a, for a shale that is likely to behave as squeezing 
ground at great depth, and the other using rock bolts, as snown in Figure 60a, 
for a highly competent granite. The following design concepts, which represent 
a conservative approach for resisting peak accelerations of 1.0g, were estab- 
lished: 168 

• It is not advantageous to harden these two systems in 
terms of stiffening them. An approach of maintaining 
flexibility is the better one. The incremental effort 
associated with dynamic loads should be focused on the 
quality of the details of the support and reinforce- 
ment systems selected for static loads and on the pre- 
vention of possible spalling or popping of rock blocks. 
In principle, a carefully executed, flexible stabili- 
zation system is preferable to a relatively stiff sys- 
tem of stabilization. Hence, attention is given to 
improving construction details to achieve a more co- 
herent medium-tunnel system. 

• Consider first the steel support system selected for 
the tunnels in shale. Inherently, this system carries 
a substantial reserve, or resilience. Both the assess- 
ment of static load and the assessment of the capacity 
of the system, derived from the squeezing-ground load 
condition, are rather conservative. A steel set seldom 
fails because the ultimate strength of a given, con- 
tinuous member of the steel set is exhausted. Rather, 
it is the failure of connections between the different 
parts of the set, or a situation of unbalanced loading, 
that results in failure of the set. Consequently, the 

- 163 - 



Steel Sets 
(W 8X58 @ 
1 m to 2 m 
on cente 



8 




Blocking 

as Necessary 



5 /S Lagging 

;f as Necessary 



Bolted 
Connections 



, - v/i VI s . 






For static load 



(scale is distorted to emphasize details) 



Steel Sets 



(w 8X58 e ^;r^}// \?&rdtt$& 

center) 35^4 



1 

on 




Continuous Blocking 
with Shotcrete 



^-Lagging 
,'with Shotcrete 
'-I Backpacking 
'^;as Necessary 

is' Welded 

Connections 



b. For static plus maximum dynamic load 
NOTE: 1 m = 3.28 ft. 



Reprinted by permission of the publisher. 



Figure 59- Tunnel stabilization system using steel sets. 
(Source: Reference 168.) 



- 164 




Rock Bolts 
(2.5 m long, 
1 .25 m on center 
each way) 



a. For static load 




Ful ly Grouted 
Rock Bolts 
(2.5 m long, 
1 .25 m on center 
/ each way) 



Reinforced 
Shotcrete 



b. For static plus maximum dynamic load 

Reprinted by permission of the publisher. 

Figure 60. Tunnel stabilization system using rock bolts, 
(Source: Reference 1 68 . ) 



- 165 



incremental support requires greater attention to con- 
struction detail and workmanship than normally would be 
required if only the static loads were considered. It 
is better to weld rather than simply to bolt together 
the different pieces of a steel set in order to estab- 
lish continuity. Steel sets should be securely tied 
together in the longitudinal direction. 

It is imperative that the ground and the support be con- 
tinuously coupled under dynamic loads. Thus, continuous 
blocking is much preferable to spot blocking. This can 
be attained by using continuous shotcrete blocking of 
the steel set and, if needed, back-packed lagging or 
reinforced shotcrete between the sets. 

• Similar considerations are applicable for the rock-rein- 
forcement systems selected for the granite. Rock-bolt 
details are improved by grouting the full length of the 
bolt. It is [preferable] to increase the amount of rock 
reinforcement by bringing it around the full circum- 
ferential area of the opening rather than springline to 
springline, as dictated by static conditions. The 
spalling of rock blocks between the fully grouted bolts 
can be prevented by the use of reinforced shotcrete. 

As stated above, the design procedure presented in Reference 168 was originally 
applied to a conceptual design study for a nuclear waste repository. 63 The 
critical nature of such an underground structure and the shortness of time and 
money for the study encouraged the somewhat arbitrary application of the full 
improvement program to the 1.0g level, as shown in Figures 59b and 60b, with 
various reductions for decreasing g-levels. The application of the full im- 
provement program to the 1.0g level is probably quite conservative. However, 
more information is needed to quantitatively relate the requirements for addi- 
tional stabilization to increases in expected peak acceleration. 

Design Based on Stress Calculations 

In the above method, 168 the simple stress calculations do not account for the 
presence of the tunnel. Dynamic stress calculations should consider two 
general situations: one in which a plane seismic wave propagates normal to 
the tunnel axis and another in which it propagates parallel to the tunnel axis. 
The first situation has received considerable interest because it results in 
dynamic stress concentrations in the circumferential stresses around the cavity. 
Furthermore, this situation can be modeled as a two-dimensional plane strain 



- 166 - 



problem that can be treated by classical methods for eirctHar -cavities and by 
finite-element or finite-difference schemes for noncircular cavities. 

The situation in which the seismic wave propagates parallel to the tunnel axis 
has not received any attention, perhaps because there are no stress concentra- 
tions associated with longitudinal stresses. However, as was pointed out in 
Chapter k, waves propagating parallel to the tunnel result in axial and curva- 
ture deformation. This may cause opening of seams and joints, possibly leading 
to rock fall. However, a numerical evaluation of stresses due to curvature 
bending cannot be modeled by a beam and would require a three-dimensional model, 
The extreme computational difficulties and high costs involved with three- 
dimensional models are very real deterrents to stress computations for this 
situation. 



Homogeneous Media . As described in Chapter k, circumferential stresses due 
to plane waves propagating normal to the tunnel axis can be calculated by 
several procedures. A simple procedure presented by Chen, Deng, and Birkmyer 
for circular cylindrical tunnels uses the free-field stresses as given by 
Equations (6) and (10) multiplied by appropriate stress-concentration factors 
depending on whether the wave is a P-wave or an S-wave and on whether the 
tunnel is lined or unlined. Many of the dynamic stress-concentration factors 
used in Reference dk were computed by Mow and Pao 65 and are shown in Figures 
20, 21, 23, and 2k. 



64 



The advantage of the analytical method presented in Reference 64 is its 
simplicity in calculating the maximum possible circumferential stresses for 
circular tunnels. These stresses may be used to evaluate the strength of the 
lining or, if the tunnel is unlined, of the rock itself. The procedure is 
based upon elastic behavior and does not consider joint properties or plastic 
response of the rock mass. Lew 68 presents a very detailed outline for the 
design of liners for circular openings in rock. The procedure was developed 
for the hardening of a deep underground structure subjected to an extreme 
shock load created by a nuclear blast at the ground surface. The load is 
visualized as a large vertical pressure induced by a compressional wave propa- 
gating downward. Conceptually this has similarities to the earthquake load, 
except that the imposed pressure from a nuclear blast will be many times 

- 167 - 



(probably many orders of magnitude) greater than the pressure from an earthquake. 
The design steps itemized by Lew follow very logically from acquisition of 
specific material and load data, to determination of liner forces, and finally 
to determination of liner thickness. Procedures are detailed for both steel 
plate and reinforced concrete liners. Because the steps are very straightfor- 
ward, they will not be reviewed here; however, a few comments are in order. 

The circumferential forces, such as springline thrust and springline bending 
movement, are determined by Lew from rock-liner interaction curves for given 
values of the medium Poisson's ratio, the medium-to-1 ine modular ratio, and 
the liner radius-to-thickness ratio. However, the curves are not derived using 
a dynamic wave loading but rather using a static pressure equivalent to the 
peak dynamic pressure. In Chapter k it was noted that maximum stress concen- 
tration, for the unlined cavity, is about 10% to 15% greater in the dynamic 
case than in the static case and that this corresponds to long wavelengths 
approximately 25 times the cavity radius. Thus, the rock-liner interaction 
curves contain an unknown amount of nonconservatism for long wavelengths. 

Lew discusses the basic concepts by which a steel or reinforced concrete 
liner maintains the stability of an opening in rock under shock loading. For 
steel liners used in protective structures, Lew has these comments: 

These liners are usually grouted into place with a cement 
mortar. The cement mortar acts as a filler, filling in 
the space between the liner and rock and providing essen- 
tially continuous contact between the liner and the rock. 
The continuous contact reduces the circumferential bending 
moments induced in the liner by the rock. Irregular con- 
tact between the liner and adjacent rock causes high, 
localized circumferential bending moments in the liner. 
Moreover, these high bending moments may cause the liner 
to buckle locally and collapse. 

Note the great similarity in these concepts with those propounded by Owen, 
Scholl, and Brekke. 16a Furthermore, Lew added these comments on reinforced 
concrete liners: 68 

A reinforced concrete liner does not tend to attract forces 
in the rock mass unless it is exceptionally thick and over- 
reinforced because its modulus is about the same order of 
magnitude as that for most competent rock masses. Within 



- 168 - 



certain limits, the bending strength of a R/C liner can be 
increased, as required, by increasing the amount of steel 
reinforcement. 



Although these comments are made in the context of design for extreme shock 
loading, they are conceptually applicable to earthquake loadings. 

Nonhomogeneous Media . When important discontinuities exist in the rock mass 
around the cavity or when the cavity is noncircular in cross section, the 
above-mentioned models can provide only very approximate values for the 
seismic stresses. In these situations, two-dimensional finite-element or 
finite-difference models become very useful tools for evaluating seismic 
stresses around cavities. Examples of finite-element and finite-difference 
codes and examples of their applications are given in Chapter k. The use 
of these methods to model elastic and elastic-plastic behavior of continua is 
very common. However, models that incorporate various important rock mass 
properties, such as joint slip, 'strain softening, dilatancy, and tensile 
cracking, are still being developed (as noted in Chapter k) and are not gener- 
ally available for analysis of rock cavities. 

The accuracy of the stress computation is not only limited by the ability of 
the model to accurately represent the behavior of the rock mass but also by 
the uncertainties in the geology. The rock mass is such a variable material 
that data collected at a few discrete points cannot possibly provide an accurate 
description for the entire rock mass under consideration. Consequently, a 
probabilistic description of the geology would be a desirable approach to 
rock tunneling. Such an approach has been suggested for evaluating alternative 
strategies for construction of rock tunnels. 169 In the area of seismic evalu- 
ation of rock cavities, Dendrou introduced uncertainty analysis into a finite- 
element calculation. 170 Dendrou expressed uncertainty in the geology by 
statistical variations in the modulus of elasticity, the Poisson's ratio, and 
mass density. Uncertainty was introduced into the dynamic behavior of the 
finite-element model by perturbing the natural frequencies of the model. Dendrou 
demonstrated that the application of uncertainty analysis and decision theory 
for seismic evaluation of rock tunnels is feasible. However, the experience 



169 - 



with this approach is so limited to date that there is little to guide the 
designer. 

Special Design Considerations 

Portals . The review of the effects of shaking on rock tunnels in Chapter 3 
indicates that portals are vulnerable to damage. Although the literature does 
not contain any references to seismic design considerations for portals, there 
are certain obvious procedures a designer might follow. Some portals have been 
damaged by rock or soil slides; therefore, a careful evaluation of the seismic 
stability of the rock or soil slopes above and adjacent to the portal should be 
undertaken. Since rock tunnels sometimes emerge at the ground surface through 
surficial soil deposits, the portal structures may actually be serving as soil- 
retaining walls. In such cases, the retaining structures should be designed 
by the Mononobe-Okabe theory. 150 

Caverns . Large caverns, such as those required for underground power plants 
or oil reservoirs, are generally excavated from hard competent rock that can 
be reinforced with rock bolts and/or shotcrete if needed. In general, the 
same concerns and design procedures described above for rock tunnels also 
apply to caverns. A potential concern in large caverns would be the movement 
of large rock blocks into the opening during seismic motion because the dimen- 
sions of the opening will exceed the spacing between joints in major sets of 
discontinuities. A thorough geologic survey of the joint systems is required. 
Attention should be given to improving the details of the rock reinforcement 
to achieve a more coherent medium-cavern system. 

Finite-element and finite-difference models can be very effectively applied 
to caverns, perhaps more so than to tunnels. Because caverns are usually 
shorter than tunnels and house critical facilities, extensive explorations of 
cavern sites are justified. A computer model for a cavern can usually be 
more detailed than one for a tunnel because more geologic information is 
available. Furthermore, a single model is much more representative of a 
cavern than a long tunnel. An example of a seismic evaluation of a rock 
cavern using a computer model is presented by Yamahara et al. 7 ^ 



- 170 - 



UNDERGROUND STRUCTURES INTERSECTING ACTIVE FAULTS 

When a tunnel crosses an active fault, it Is not possible to design the tunnel 
to withstand a potential offset in that fault. However, special design fea- 
tures can be incorporated to facilitate postearthquake repairs and reduce the 
extent of the damage. Examples of such design features are given below for 
three projects. In addition, special design features recommended for box 
conduits are presented. 

Case Studies of Special Design Features 

California State Water Project . The design philosophy in the California State 
Water Project was to cross major active faults either at the ground surface or 
at very shallow depths. » 1 This would facilitate repair in case of damage 
resulting from movement along a fault. The philosophy played an important role 
in determining the alignment of the California Aqueduct through the Tehachapi 
Mountains. Two basic alignments were originally considered for crossing these 
mountains: a low-level alignment, which would allow a relatively low pump lift 
at the southern end of the San Joaquin Valley, and a high-level alignment, 
which would allow a series of relatively short tunnels. The low-level align- 
ment would have resulted in a long tunnel penetrating several major faults at 
great depth and would have resulted in adverse tunneling conditions and high 
construction costs. But the major reasons for not adopting this alignment 
were the extreme difficulty and high cost of repairing damage to the tunnel 
due to movement along one of the major faults. In spite of the high cost of 
lifting the water, the high-level alignment was chosen so that faults could 
be crossed at or near the surface. This also resulted in shorter tunnels and 
more favorable tunneling conditions. 

In the final selection of the high-level alignment, only the Garlock fault was 
crossed underground. The south branch of the Garlock fault at Beartrap Canyon 
is crossed by the Beartrap access structure. This structure is a buried rein- 
forced concrete conduit, 20 ft (6.1 m) in diameter and 315 ft (96.0 m) long, 
providing the connection between Tunnel No. 3 and the Carley V. Porter Tunnel. 
Details of this structure are provided by the profile and plan in Figure 61 
and the typical cross section in Figure 62. The information given in these 



171 - 




00 

-a- 
o 

O 
II 



E 
o 

-a- 
irv 

II 






o 

c 

0) 

<u 

0) 

a: 



a) 
o 

i_ 

3 

o 



1_ 

3 

o 

3 



•A 

<a 
o 
o 
<o 

Q. 
<0 

l_ 
+-> 
l_ 
<TJ 

a) 

CO 

U 

O 



O 

i_ 
o- 

a) 

i_ 

3 
en 



172 - 



T-6 



5'~0' 



~Syn% about § 



Cons true t. 'on 
Joint 




•69IZ 



Lap splicer to 
bo st*99ere*' 
mt Won miff- 
nmte no*** 



Concrete mud stab 



Scale 1/V = V 

NOTE : 1 in. = 2.5 / » cm; 1 ft = 0.3048 m. 

Figure 62. Typical section of Beartrap access structure, 
(Source: Reference 173.) 



- 173 - 



figures is derived from Reference 173- The north branch of the Garlock fault 

is also crossed, but on the ground surface. This crossing, known as the 

Pastoria Siphon, consists of a 0.5-mile (0.8-km) long steel conduit with an 
inside diameter of 16 ft (k.S m) . 

SFBART . When a rock tunnel must cross an active fault, the tunnel might be 
made oversized through the fault zone. This approach was taken by SFBART where 
the train system crossed the Hayward fault in the Berkeley Hills between Oakland 
and Orinda. "The tunnel was made slightly oversized and was lined with closely 
spaced steel rib sections, to permit absorption of tectonic deformations and 
promote rapid repair and realignment of track in the event of any major shift 
along the fault. " 17lf 

East Bay Municipal Utility District . A rock tunnel used for the conveyance 
of water presents special problems if it crosses a fault that undergoes a major 
offset. Apart from having to drain the tunnel, rapid repairs to the tunnel may 
have to be made following an earthquake. The East Bay Municipal Utility District 
(EBMUD) of Oakland, California, has made extensive preparations for a major 
earthquake. 175 EBMUD' s 10-ft (3 - m) horseshoe-shaped Claremont tunnel crosses 
the Hayward fault in the Berkeley Hills. To facilitate repairs in the event of 
future slip along that fault, EBMUD modified the access structures at each end 
of the tunnel in 1 967 - Furthermore, steel sets and other materials essential to 
the rapid repair of this tunnel (and other facilities as well) have been stock- 
piled. 176 

Recommendations for Special Design Features of Box Conduits 

Some special construction features may be useful in mitigating the damage to 
a reinforced concrete tunnel in soil. Hradilek studied the damage to two 
underground box conduits, the Wilson Canyon and Mansfield Street boxes, due to 
the San Fernando earthquake of February 9, 1971. 29 '» 177 The Wilson Canyon box 
is intersected by the Sylmar segment of the San Fernando fault zone, which at 
that point experienced a left-lateral slip of about h ft (1.2 m) and a reverse 
dip slip of almost 8 ft (2. k m) . The Wilson Canyon box was severely damaged 
for a length of about 300 ft (91 m) by this thrusting and shearing. In addition, 
about another 200 ft (61 m) of the box to the north of this zone suffered major 



- 174 - 



cracks and separation because the soil in that region experienced a permanent 
extension. The damage to the Mansfield Street box was confined to a short 
length of 50 ft (15 m) adjacent to its confluence with the Wilson Canyon box 
due to compressive shortening of about 7 in. (18 cm). Although there were no 
surface expressions of faulting in that area, the damage was attributed to 
fault movement. The alignment of the two boxes is col i near; however, the 
Wilson Canyon box has a short branch off to one side that connects to an up- 
stream open channel just at the point of confluence. Hradilek suggests that 
this jog offered resistance to longitudinal movements in the Mansfield Street 
conduit resulting in a local manifestation of compression crushing at that 
point. 

From these observations, Hradilek offers several useful suggestions for the 
design of reinforced concrete conduits crossing a known active fault zone: 177 

• Seismic joints should be closely spaced. Spacings of 
30 ft (9 m) or less are suggested, but Hradilek notes 
that this is based on very limited data. The seismic 
joints provide weak bands around the box but maintain 
minimum strength during normal static conditions. Dur- 
ing fault slip the seismic joints absorb the movements 
by separating or crushing. The seismic joint is formed 
by providing a void or crush-space with a wood form or 
friable masonry blocks as shown in Figure 63. 

• Construction joints and seismic joints in the invert, 
walls, and soffit should all occur in the same verti- 
cal plane. The shear resistance R • of the joint and 
the length La between the joints snould be such that 
2Rj 5 qL., wnere q is the least transverse design load 
per unit length of the box. The use of shear keys in 
vertical joints is discouraged. 

• If large displacements are anticipated, the conduit 
should be oversized. 

• Changes in the geometry or properties of the cross sec- 
tion, sudden changes of direction, and confluence 
should be avoided in an active fault zone. 



175 



Extend dowels past this point 
only as needed for minimum 
strength. Stop all other bars. 



n u 



M 



iryjss-s-ss ^^■k^rT-^r 



N 
N 
N 

; 
) 






J\W\\\\ 



"^Tp^y 



h 



i 



a * » a « » ^ 



\ 



0»W 

Wood Form for Void 
(to be left in place) 



wmn 



Extend dowels past this point 
only as needed for minimum 
strength. Stop all other bars 



Bond 
Breaker" 




Water Stop if Required 



i » 5 ■ a 8 a 



4 



i // n n n n ri 7 



Lightweight Concrete Masonry Unit 
(do not join with mortar) 



— W /; " 

Water Barrier if Required 



Figure 63. Proposed seismic joint for reinforced concrete conduit 

(Source: Reference 29.) 



- 176 



7. Critique of the State of the Art 

The previous chapters discussed in considerable detail what is known about 
seismic damage to underground structures, the nature of underground motion, 
and the available technologies for analysis and design. The information 
presented constitutes the state of the art of earthquake engineering for 
underground structures. In this chapter, we shall indicate the areas where 
data and techniques are generally adequate and those where they are not. 

EFFECTS OF EARTHQUAKES ON UNDERGROUND STRUCTURES 

More data on the response of underground structures to earthquake shaking have 
been collected for this study than have been collected for any other single 
report. The data expands our understanding of the seismic vulnerability of 
various types of underground structures in different geologic settings. In 
general, the reported damage to underground structures is less severe than 
damage to surface structures at the same location. Damage to underground 
structures from shaking is generally minor, although major damage, meaning a 
large cave-in or closure, sometimes occurs. 

This study has indicated that the type of data available is not sufficient to 
determine the relative importance of various parameters for predicting damage 
or lack of damage. The important parameters that influence the earthquake 
behavior of underground structures are identified in Chapter 3« These param- 
eters are cross-sectional dimensions, depth below ground surface, strength and 
other characteristics of the rock or soil, support and lining systems, and 
severity of the shaking. The ground shaking at the site can be characterized 
by peak ground motion parameters, duration, frequency content, and intensity. 
At this time, it» is not clear whether damage should be correlated with peak 
acceleration or with peak particle velocity; however, intuition suggests that 
correlation with peak acceleration is better for massive concrete structure's 
in soil and that correlation with peak particle velocity is better for hard 
rock openings. Duration of the shaking is believed to be an important factor 
in that longer duration is expected to correlate with greater damage, particu- 
larly for buried concrete structures. Frequency content of the vibration may 



- 177 - 



also be important because some researchers suspect that damage to openings in 
rock is associated with wavelengths on the order of twice the cavity dimensions. 
These parameters have not been sufficiently studied in previous studies of 
observed effects, and it has not been possible in the confines of this study 
to collect information on all the parameters for the 127 cases cited in 
Appendix C. 

The historical data base on the response of underground structures to earth- 
quakes, while significantly larger than any reported elsewhere, is really a 
very small base from which to draw hard conclusions. The small size of the 
data base is in extreme contrast to the volumes of data recorded about the 
performance of surface structures during earthquakes. One of the reasons for 
this is that there are fewer tunnels, underground caverns, and other large 
underground structures than surface structures in the epicentral regions of 
most major earthquakes. Probably an even more important reason is the apparent 
lack of systematic surveys of underground facilities following major earthquakes. 
In general, damage to surface structures is more dramatic than damage to under- 
ground structures and is, of course, much more visible. As a consequence, 
reconnaissance teams sent to survey damage after major earthquakes are usually 
composed of engineers primarily interested in surface structures. This situation 
needs to be changed by establishing teams to survey underground structures follow- 
ing major earthquakes. 

UNDERGROUND SEISMIC MOTION 

Information on seismic motion recorded at depth (in boreholes, tunnels, mines, 
etc.) has been thoroughly reviewed in this study. These data indicate a general 
trend in the reduction of peak acceleration with depth, although records exist 
of peak amplitudes at depth that were greater than those at the surface. The 
records from layered soil deposits indicate amplitude amplification at the 
ground surface with respect to base rock for selective frequencies associated 
with the natural frequencies of the soil layers. This phenomenon seems to be 
well understood and can be modeled fairly well mathematically. However, the 
variation of amplitudes within rock at great depth seems to be poorly understood. 
For many decades, data were sparcely collected; only within the past several years 
have data been collected in a systematic way. Clearly many more records will have 

- 178 - 



to be obtained at depth before better descriptions can emerge as to variation 
of motion amplitudes and frequency content with depth. 

Mathematical models could perform a useful function in helping us to understand 
the basic nature of underground motion. By using a very simple wave propagation 
model (SH-waves in an elastic half-space) in this study, we found that the varia- 
tions of peak amplitudes with depth are strongly dependent upon the characteris- 
tics of the time history (in particular the temporal dispersion of peaks of 
approximately the same amplitude) and the duration of the motion. Much greater 
understanding could be obtained by employing more sophisticated models in con- 
junction with the further collection of recorded motion. 

The importance of a good collection of data concerning the characteristics of 
underground motion and concerning the behavior of underground structures to 
seismic motion cannot be overstated. The development of earthquake engineering 
technologies for underground structures will only make significant advances 
when our understanding of underground motion and its effects on underground 
structures is adequately founded on observation. An analogy may be drawn with 
earthquake engineering of surface structures, which did not begin to approach 
the general level of present-day sophistication until after the recording and 
analysis of many time histories of strong surface motion and the detailed 
observation of buildings damaged by earthquakes. The state of the art of 
earthquake engineering of underground structures may be where the state of 
the art of earthquake engineering of surface structures was 20 to 25 years ago. 

CURRENT PRACTICE IN SEISMIC DESIGN OF UNDERGROUND STRUCTURES 

Seismic Design of Subaqueous Tunnels 

In Chapter 6, the various methods currently used for the analysis and design of 
underground structures are reviewed in terms of subaqueous tunnels, structures 
in soil, and structures in rock. Of the three, the current methods for the 
analysis and design of subaqueous tunnels are the most sophisticated. This is 
because the submerged tube is constructed from highly predictable materials, 
such as reinforced concrete and steel, and does not depend upon the highly 
variable geologic medium to maintain the strength and stability of the opening. 



- 179 - 



In this way, the subaqueous tube is similar to surface structures. Consequently, 
the seismic design methodologies have been drawn from contemporary analytical 
technologies and up-to-date procedures for the design of steel and reinforced 
concrete surface structures. 

Seismic Design of Underground Structures in Rock 

Structures in rock differ from subaqueous tunnels in that the geologic medium 
is a major component of the structure. In fact, in cases where the rock does 
not require support or reinforcement, the geologic medium is the structure. 
The technologies for analyzing the seismic stability of an opening in rock and 
for determining hardening procedures are poorly developed. One reason for this 
retarded development is that there are very few reports of major damage to 
openings in rock from earthquakes, and therefore designers usually ignore this 
potential failure mode. 

Perhaps the most significant reason that earthquake engineering technologies 
are so poorly developed for rock openings is that the state of the art in 
static design of such openings is itself still in its infancy. The relationship 
between the static and seismic design methods can be best understood by refer- 
ring to Table 5 and Figure 64. 

The available technologies for static and seismic design take sharply different 
approaches depending upon whether the rock mass is assumed to be homogeneous 
and elastic or is assumed to be nonhomogeneous and inelastic. If the rock is 
assumed to be homogeneous and elastic, compatible procedures exist for the 
analysis of both static and seismic stresses. The Kirsch's solution is used 
to determine the stresses in homogeneous, elastic rock around circular openings 
due to the in situ stress field. Terzaghi and Richart used the Kirsch's solution 
to compute the distribution of stresses around a circular tunnel for a case in 
which the horizontal in situ stress was 0.25 times the vertical in situ stress, 
which corresponded to a Poisson's ratio of 0.20. 178 (Terzaghi and Richart also 
presented solutions for elliptical tunnels and spheroidal cavities.) Mow and Pao 
have determined the dynamic stress-concentration factor for the circumferential 
stress in homogeneous, elastic rock around a circular tunnel due to steady-state 
harmonic waves. 65 In an analysis for earthquake motion, the maximum stress 
around the opening can be estimated by multiplying the peak seismic stress in 

- 180 - 



Table 5. Compatibility of earthquake design methods 
with static design methods for openings in rock. 



Description of 
Geologic Medium 


Static Design 
Method 


Earthquake Design 
Method 


Homogeneous 
and elastic 


Two-dimensional stress 
analysis solutions 
avai lable (For ci r- 
cular and ell ipt ic 
tunnels, see Reference 
178.) 


Two-dimensional stress 
analysis solutions 
avai lable (For ci r- 
cular tunnels, see 
Reference 65.) 


Nonhomogeneous; 
•various degrees 
of rock fractur- 
ing, joint incl i- 
nation, etc. 


Empirical methods 


Some initial 
development 168 


Simple analytical 
methods 


? 


Rigorous analytical 
methods (i.e., f ini te 
element and finite 
d ifference) 


Some initial 
development (finite 
element and finite 
difference) 



- 181 - 



<U 




> 




■M 




ro 




0) 




cc 


+J 




c 


M- 


cu 


O 


E 




a. 


1 — 


O 


0) 


w— 


> 


d) 


<u 


> 


_! 


(1) 







■M 




c 




0) 




1_ 




1_ 




=> 




CJ 





J L 



Static Design Methods 



Seismic Design Methods 



Empi r ical 
Methods 



i — I 



Simple 

Analytical 

Methods 



Rigorous 
Analyt ical 
Methods 



Figure 64. Comparison of current level of development between 

the various design methods. 



182 - 



the free field (determined from the peak particle velocity of the earthquake) 
by the Mow and Pao dynamic stress-concentration factor as described in Chapter k. 
Thus, for circular tunnels in homogeneous, elastic rock, the methods for the 
analysis of static and seismic stresses are quite compatible, and the design 
can be evaluated by comparing the sum of the static and seismic stresses to 
the rock strength. 

Even for noncircular openings, compatible static and seismic design technologies 
exist for homogeneous, elastic rock. Static stresses around such an opening 
can be computed by various contemporary approaches, such as finite-element, 
finite-difference, or boundary-element methods. Seismic stresses can also be 
computed using propagation of the earthquake motion with some of these same 
methods. 

Real rock masses are not homogeneous and do not behave in an elastic manner. 

A number of empirical and analytical methods are available for the static design 

of tunnel supports in real rock masses. The empirical methods include Terzaghi's 

1 7 Q 1 ft 

rock load approach/ the new Austrian tunneling method of Rabcewicz, and the 
methods by Barton et al., 181 Bieniawski , 182 and Wickham et al., which use a 
number of parameters to quantify the geology. These and other empirical methods 

1 84 

have been reviewed in a recent paper by Einstein et al. Sophisticated analy- 
tical methods, such as finite-element analysis, have been applied to both two- 
dimensional and three-dimensional analyses of tunnels in jointed rock (for 
example, References 184 and 185). While the application of rigorous analyses 
requires accurate and detailed information on the geology and the development 
of appropriate constitutive models, the application of empirical methods, which 
are based on actual observations of prototype openings, does not require such 
detailed quantification of the geologic information. In the design of an under- 
ground opening, the information on the geology is usually very limited prior to 
excavation, thus favoring empirical methods. During construction, although the 
information about the geology has greatly increased, decisions regarding the 
initial support must be made rather quickly, which also favors the use of 
empirical methods over analytical procedures. Consequently, there is a much 
greater dependence upon empirical methods and with that a much greater develop- 
ment of empirical methods. A third type of method — a simplified analysis — 
has been developed for circular tunnels. This method uses limited quantitative 

- 183 - 



data on the geology in conjunction with a simple but rational analytical model 
to determine support requirements. 164 Conceptually, the simplified analysis 
falls between the empirical and rigorous analytical methods. It should be 
noted that this discussion of static design of openings in rock is not intended 
to be complete, but only to indicate the general nature of the design methods. 

In the design of supports for openings in real rock conditions, few seismic 
methods exist that are compatible with the existing empirical and analytical 
methods in static design. The only seismic design method that is compatible 
with the empirical methods for static design is the one proposed by Owen, 
Scholl, and Brekke, 168 which is based upon a qualitative assessment of rock- 
support interaction and upon the empirical relationship between damage to rock 
tunnels and peak ground motion parameters of earthquakes. Seismic methods com- 
patible with rigorous analyses for static stresses are based on the same pro- 
cedures as the static methods (for example, finite-element and finite-difference 
methods), but at this time rigorous analyses for seismic stresses for openings 
in rock have not progressed beyond preliminary developmental stages. 

Clearly seismic design technology is poorly developed for openings in rock. The 
significance of this poor development is relative to the function and location 
of the structure and the condition of the rock. While most rock openings prob- 
ably will not need to be evaluated for seismic stability, structures located in 
areas with moderate to high seismic hazard should be evaluated. The need for a 
seismic evaluation becomes more emphatic if collapse of the opening could lead 
to major loss of life or could severely disrupt lifelines. Structures that 
perform very critical functions — for example underground nuclear power plants 
and nuclear waste repositories — require seismic evaluations regardless of the 
degree of seismic hazard. 

Seismic Design of Underground Structures in Soil 

A distinction must be made between cut-and-cover structures and soil tunnels 
that are excavated by tunneling methods. Cut-and-cover structures are generally 
reinforced concrete structures at shallow depths. Static loads are determined 
by conventional soil mechanics, and static designs follow the same well- 
established procedures that are used for reinforced concrete structures on 
the surface. Thus, the earthquake design procedures presented in Chapter 6 

- 184 - 



to design soil structures for deformation and increased soil pressure are com- 
patible with static design practice for cut-and-cover structures. 

The static design of soil tunnels is very different from that of cut-and-cover 
structures, partly because soil tunnels are usually deeper and often below the 
water table but more importantly because of the different construction methods 
used for soil tunnels. Tunnels excavated through stiff soils can be initially 
supported by steel ribs and lagging, with permanent concrete liners installed 
later. In contrast, tunnels in poor soils might require excavation with the 
aid of a shield and immediate lining with concrete or steel liner segments. 
The final static loads on the supports for a soil tunnel are determined by the 
principles of soil mechanics; 186 ' 187 however, the static design of liner segments 
for shield-driven tunnels is often governed by the forces required to jack the 
shield forward. Sometimes the hydrostatic water pressure on the final tunnel 
may be a much larger concern than the loads due to the soil. These brief com- 
ments on the static design of tunnel supports in soils are presented only for 
a general frame of reference and not for completeness. 

Design of soil tunnels is very similar to that of rock tunnels. Because 
information on the soil prior to excavation is sparce and the time in which 
to make design decisions about support during construction is limited, there 
is a heavy reliance upon past experience with prototype structures. In this 
respect, the relationship between earthquake design methods and static design 
methods for soil tunnels is similar to that for rock tunnels; the methods are 
not entirely compatible and are very poorly developed at this time. 



- 185 - 



8. Recommended Research Activities 

This assessment of the state of the art of earthquake engineering of large 
underground structures has led to the identification of several major research 
needs. These needs are summarized below, and specific research activities are 
suggested in answer to these needs. 

The research activities will provide information essential to the design of 
critical underground structures. The design of repositories for the disposal 
of nuclear waste and toxic chemicals will require seismic evaluations regard- 
less of the level of seismic hazard. Transportation tunnels, aqueducts, and 
other underground structures whose failure during an earthquake could seriously 
imperil public health and safety must be designed for earthquakes in regions of 
high seismicity. 

The research activity with the highest priority is the collection of data on 
the effects of earthquakes on underground structures. These data will help to 
identify the conditions that lead to damage and to predict the types of damage 
that are likely to occur. Research activities directed toward the development 
of rigorous analytical and design methodologies are not as high a priority as 
those activities directed toward obtaining observational data. The develop- 
ment of these methods could wait until a design project arises that demands 
the application of rigorous procedures, although such postponement will not be 
particularly cost effective. 

OBSERVED EFFECTS OF EARTHQUAKES ON UNDERGROUND STRUCTURES 

It has been noted in the previous chapter that the data about the effects of 
earthquakes on underground structures form too small a data base from which to 
draw hard conclusions. In addition, the data needed for a definitive evalua- 
tion of the influence of various factors on damage to underground structures 
are not readily obtainable for past earthquakes. The parameters that are 
believed to influence the response of underground structures and about which 
information should be collected are as follows: 



186 



Cross-sectional dimensions of the opening 

Depth of the structure below the ground surface 

Type of rock or soil, including strength and 
deformabi 1 ity characteristics 

Type and condition of the support and lining system 

Shaking severity, characterized by peak ground motion 
parameters, duration, frequency content, and intensity 

Another situation that affects the usefulness of damage reports is the general 
lack of inspections of structures before an earthquake. Sometimes it is diffi- 
cult to determine whether minor cracks in concrete lining or movements of steel 
sets resulted from the earthquake motion or were due to other events and existed 
prior to the earthquake. 

It is often very difficult to obtain all the needed information indicated above, 
even for fairly recent events. Because some of the most useful information can 
be obtained from technical and lay persons close to the scene (perhaps more than 
from reports that have been prepared by outside reconnaissance teams), the more 
time that has elapsed since an earthquake, the less information can be obtained. 
Thus, efforts would best be spent on studying only very recent earthquakes (say, 
within the last ten years) and on preparing plans to conduct more thorough 
surveys of underground structures in future earthquakes. It is from this 
viewpoint that three experimental research activities are recommended. 

Research Activity 1: Comprehensive Survey of Earthquake 
Effects on Underground Structures 

A systematic study of all underground structures in the epicentral regions of 
recent destructive earthquakes should be undertaken on a worldwide scale. 
Detailed information should be collected on the earthquake and the underground 
structure (the ground and the support) so that comprehensive entries can be 
made in all columns of a table such as Appendix C. To provide the best oppor- 
tunity for obtaining definite conclusions, the study should be limited to 
earthquakes that have occurred within the past ten years. The objectives of 
the study would be to initiate the establishment of a detailed data base and 
to formulate more definitive conclusions about how the various parameters 
affect damage or lack of damage. 



- 187 - 



Research Activity 2: Postearthquake Reconnaissance of 
Underground Structures 

In the future, when a destructive earthquake occurs, special reconnaissance 
teams should be sent to the affected region to survey underground structures. 
It is recommended that the reconnaissance teams convened and dispatched to 
earthquake-devastated regions by such agencies as the U.S. National Science 
Foundation or the Earthquake Engineering Research Institute include among 
their members several people specifically delegated for surveying underground 
structures. Underground structures that should be surveyed include -highway 
tunnels; railroad tunnels; fresh water tunnels (although if the tunnels are 
still operational, visual inspection will be impossible); tunnels and conduits 
that serve as major collectors for storm water and wastewater; subways; buried 
water reservoirs and water treatment facilities; powerhouse caverns; and 
storage facilities. Some of these structures are important components of life- 
line systems and should be surveyed anyway. Data should be collected in as 
much detail as possible and with the intent to complete a table with headings 
similar to those given in Appendix C. It is important that all underground 
structures be included in the survey, not just those that are damaged. Thus 
the survey will provide a data base from which meaningful and definitive 
conclusions can later be formulated about the relationships of the various 
parameters and the extent or lack of damage. 

Research Activity 3: Observations of Selected Tunnels 
Before and After Earthquakes 

It is recommended that preearthquake observations be conducted in a number of 
tunnels so that it will be possible to distinguish between cracks, movements, 
and other damage due to nonearthquake sources and those due to an earthquake, 
should one occur. Of course, sites in regions of high seismic activity should 
be selected to increase the likelihood of being able to observe the results of 
a major earthquake within several decades. 

A program of this type was proposed in a report by Brekke and Korbin to promote 
early installment of relatively simple instrumentation in a few selected tunnels 
in California. 188 The report suggested four levels of instrumentation with 
increasing sophistication. The basic level concerned the kinds of preearthquake 
observation envisioned here. (The other three levels involved the installation 

- 188 - 



of triaxial accelerometers. ) Brekke and Korbin suggested that the following 
basic observations and measurements be conducted for a length of approximately 
100 ft (30 m) along a tunnel: 188 

• All defects in the support/lining system that can be 
observed at present should be carefully mapped either 
through sketches and/or through photographs. The 
orientation, length, and offset of cracks should be 
documented. Plaster can be placed occasionally over 
cracks to serve as an indicator of subsequent dis- 
placement. 

• Measuring points for tape extensometer readings should 
be installed [at appropriate locations around the 
tunnel perimeter]. The points can be balls, rings, 

or pins, depending on the type of tape extensometer 
that is employed. After installation, careful ex- 
tensometer readings shall be made, and repeated as part 
of the maintenance program (i.e., at least once a year) 
to check for possible deformations that are not earth- 
quake induced. 



Brekke and Korbin proposed three candidate tunnels in California for instrumen- 
tation: the Loleta Railroad Tunnel No. 40 in Humboldt County, the Caldecott 
Tunnel in Alameda County, and the San Fernando Railroad Tunnel No. 25 in 
Los Angeles County. At this time, these basic observations and measurements 
are being conducted in only the Caldecott Tunnel (along with the installation 
of some triaxial accelerometers). 

UNDERGROUND SEISMIC MOTION 

This study has thoroughly reviewed the available information on seismic motion 
at depth and concluded that the characteristics of underground seismic motion 
are poorly understood, except for motion in horizontal soil layers near the 
ground surface. Until recently researchers have obtained very few underground 
records, and most of those have been obtained in Japan. Additional strong 
motion instruments have been installed underground in recent years, mostly in 
Japan, where there is now a network of approximately 200 underground instru- 
ments; only a few installations exist in the United States and elsewhere. The 
published accounts of the records obtained to date indicate a general reduction 
of peak acceleration with depth, although there are instances where amplitudes 
at depth are greater than those at a more shallow depth or at the surface. At 

- 189 - 



this time, not enough data have been collected to provide a reliable predictive 
model or to address the anomalies of the variation of motion with depth. 

Several other issues concerning underground seismic motion also remain poorly 
understood. The difference between the frequency content at depth in rock and 
at the surface and the role of frequency on depth dependence of motion amplitudes 
have been explored in the literature, but nothing definitive has been forth- 
coming. Some underground instruments have been placed in transportation 
tunnels, mines, and powerhouse caverns, but apparently only for the convenience 
of obtaining an underground site. There have been no attempts to compare the 
motions recorded in such structures with free-field motion in the nearby rock 
or soil at the same depth. Differences in motion between the underground 
structure and the free-field would indicate the manner in which the structure 
is responding to the motion. 

It has already been noted (in Chapter 7) that mathematical models could perform 
a useful function in helping us understand the characteristics of underground 
motion. Unfortunately, it is difficult to represent the complexities of geology 
and wave types, and therefore only the simplest situations have been studied 
thus far. 

The most obvious conclusion to draw from these observations is that a more 
aggressive program is needed in the United States for the recording of under- 
ground motions. Before recommending specific research activities for such a 
program, the general characteristics of instruments shall be discussed. In 
general, constraints on the fidelity of strong motion records are imposed by 
the type of transducer or seismometer rather than by the recorder. 

Although velocity-sensitive transducers are desirable from the data processing 
viewpoint of ease of conversion to acceleration or displacement by either a 
single differentiation or integration, they have inherent low-frequency 
response limitations. A velocity-sensitive transducer must be physically large 
(and relatively expensive) to have a flat response much below 1 Hz. Nonlinear 
response at low frequencies can be corrected in the recording stage by elec- 
tronic compensation or during data processing, but this complicates the system. 
Another constraint on velocity sensors is imposed by the mechanical limits of 

- 190 - 



coil-to-case motion in the transducer itself. A reasonably priced sensor 
(approximately $1,000 in 1979) that has a natural frequency of 1 Hz and that 
is 0.7 critically damped will reach its limit at a displacement of only about 
0. 24 in. (0.6 cm), zero to peak. This constraint is a serious one if the seismic 
environment suggests a reasonable probability of exceeding this level of ground 
displacement. For example, a moderate-size earthquake will probably generate 
considerable motion in a frequency band from 1 to 5 Hz; for a peak particle 
velocity of approximately k in. /sec (10 cm/sec), the displacements will range 
from 0.12 to 0.63 in. (0.3 to 1.6 cm). 

Accel erometers do not have a limit on the amount of displacement they can 
tolerate. Force-balance (or servo) accelerometers will respond down to DC and 
can easily handle the anticipated levels of strong ground motion. Dynamic 
stress-concentration factors for circular cavities (discussed in Chapter k) are 
highest for the low frequencies between DC and about 10 to 15 Hz, the upper 
value depending upon the wave speed and the cavity radius. Higher frequencies, 
corresponding to wavelengths on the order of two times the cavity dimension, 
may also be important to cavity behavior. Thus, it is desirable for the 
instrument to be able to respond from DC to about 100 Hz, which is within the 
capabilities of current accelerometers. 

Accelerometers require a very stable power supply in contrast to the typical 
velocity-sensitive transducer, which is self-generating and requires no external 
source of power. Although the use of accelerometers would sacrifice some of the 
simplicity of data acquisition and processing provided by velocity-sensitive 
transducers, the broad dynamic range of accelerometers makes them the preferred 
type. 

There are several digital recorders on the market that are specifically designed 
and admirably suited for the proposed task. All of them have the capability of 
continuously accepting motion data but recording only motions that exceed a 
predetermined threshold; all the data, including data for the quiescent period 
prior to the onset of motion, are preserved by means of introducing delay buffers 
between the incoming signal and the output to the recording mechanism. 



191 



The cost of a triaxial seismometer package consisting of three accelerometers, 
three amplifiers, and a three-channel recorder is approximately $7,000 (in 1979 
dol lars) . 

Research Activity k: Recording of Seismic Motion 
in Deep Boreholes 

It is recommended that a program be undertaken to record and evaluate underground 
motions in boreholes down to depths of approximately 3,000 ft (approximately 
1,000 m) . Although shallow depths of just several hundred feet are of interest 
for shallow structures and for interaction between soil and surface structures, 
greater depths are important for understanding the nature of the motion arriving 
at deep tunnels and powerhouse caverns. A suite of four or five triaxial instru- 
ments distributed from the surface to the bottom of a deep borehole can provide 
an excellent source of data for studying the variation of motion with depth. 
The study should evaluate variations of peak values of acceleration, particle 
velocity, and displacement; the variations in frequency content; and the uphole- 
downhole spectral ratio. The ideal location for such boreholes would be in an 
area of active faulting, such as certain sections of the San Andreas fault, 
where a fair amount of data can be collected within a period of a few months 
to a year. 

Research Activity 5: Recording of Seismic Motion 
in Underground Openings 

To address the issues regarding the differences between the motion of an under- 
ground structure and the free-field motion at the same depth, an instrumentation 
program similar to that proposed by Brekke and Korbin 188 should be conducted. 
We recommend that several additional rock tunnels be selected in regions of high 
seismicity. (An actual number is not recommended, but two seems to be a minimum.) 
These tunnels, in conjunction with the al ready- instrumented Caldecott Tunnel in 
Alameda County, California, would begin to provide very useful comparative 
results after several years of observation. In selecting the rock tunnels, it 
would be useful to get different maximum covers. Because the Caldecott Tunnel 
has a maximum cover of about 500 ft (152 m) , it would be advantageous to have one 
additional tunnel at a shallower depth and, if possible, the other deeper. 



- 192 - 



Additional structures other than rock tunnels should be considered for the pro- 
gram. A large rock cavern would be an excellent choice because the geometry 
and size of the opening is quite different from a tunnel. Another candidate 
structure would be a very shallow structure in soil, such as a cut-and-cover 
subway tunnel. 

The type of instrumentation to be installed should be the triaxial accelero- 
meter and recorder package described above. In keeping with the recommendation 
of Brekke and Korbin, 188 the minimum number of triaxial accelerometers for a 
rock tunnel would be three, located as follows (see Figure 65): 

• One in the tunnel, well away from the portal region 
and, if possible, in the region of maximum cover, 
to measure the response 

• Another located in the rock mass at the same elevation 
as the tunnel instrument, to measure the free-field 
motion 

• Another located at one of the portals, to measure the 
portal response 

The free-field instrument must be located sufficiently far from the tunnel so 
that waves reflected from the tunnel will be attenuated to negligible values 
by the time they arrive at the free-field instrument. Brekke and Korbin 
suggest a distance of at least ten tunnel diameters; 188 this seems like a 
very conservative but practical suggestion. 

Instrumentation of a portal is recommended because the portal is the part of 
the tunnel most susceptible to damage. Motions recorded there can be compared 
with the free-field motion and with the tunnel responses to see if there are 
important differences in the motions that might contribute to the greater 
susceptibility to damage. 

The recording of free-field motion at the ground surface above the tunnel is 
not recommended for this program. Motion at the surface would be a poor basis 
for comparing tunnel response because of the reflection of wave energy at the 
free surface and the multiple reflection within the soil layers near the 
surface. However, because a borehole will probably have to be drilled to 
install the subsurface free-field instrument, certain elements of Research 

- 193 - 



•Ground Surface 




Tunnel Response 
Instrument 




Optional Instruments 



-Borehole 



(£ Free-Field Response Instrument 



d Q 


~\0d o 







(not to scale) 



a. Section through tunnel 



Optional Instruments 




Response Instruments 



(not to scale) 



b. Prof i le of tunnel 



Figure 65. Proposed locations of triaxial accelerometers for a tunnel 



194 - 



Activity k could be incorporated. By installing triaxial accelerometers at 
the surface of the borehole and perhaps another at middepth, a collection of 
data could be obtained to study the variation of motion with depth. 

The locations of the instruments within a large rock cavern are more specialized 
than for a tunnel. Whereas a tunnel is long and connects to the ground at the 
portal, a cavern has large cross-sectional dimensions and is limited in length. 
Because we are mainly interested in the possible differences in motion around 
the perimeter of the cavern section, there should be four instruments located 
around the perimeter (away from the ends of the cavern) on the invert, the 
crown, and the sidewalls, in addition to the free-field instrument at the 
cavern elevation (see Figure 66). 

It should be noted that the basic preearthquake observations and measurements 
proposed in Research Activity 3 should be carried out at the instrument stations 
recommended above. 

Research Activity 6: Development of Analytical Models 
for Predicting Seismic Motion at Depth 

Simple parametric studies such as those begun in this report should be continued 
as part of a program to develop analytical models for predicting seismic motion 
at depth. These efforts should be parallel to experimental efforts to under- 
stand the effects of depth upon underground motion from downhole records (see 
Research Activity k) . 

This report considered only SH-waves in an elastic half-space. Models should be 
developed by slowly increasing their ability to represent the complexities of 
the geology and the waves. Premature development of a grandiose model that 
includes many complexities will be costly and may actually obscure the basic 
behaviors of underground motion. Thus, models should be improved in a small 
incremental fashion. A first step would be to include the propagation of 
P-waves and SV-waves in an elastic half-space; later steps would involve 
improving the model with horizontal layers over a half-space. The theoretical 
basis for these later steps is provided by Thomson 189 and Haskell. 190 What is 
now needed is the application of those techniques to actual geologic conditions 



- 195 - 





Crown Instrument 



(£ Free-Field Instrument 



Sidewal 1 
I nstruments 



///A\W 



-"Invert Instrument 



Width 



10 Times Width 



Figure 66. Proposed location of triaxial accelerometers for a large cavern, 



- 196 - 



and comparisons of predicted motion at depth with experimental values. Some 

ion 

work in this direction has already been started by O'Brien and Saunier, who 
developed transfer functions for P-waves and SV-waves propagating through a 
single layer over a half-space. O'Brien and Saunier applied the model to an 
actual site and compared theoretical predictions of motion at depth with 
experimental values. Another step leading to improvement in the model would 
be to include nonlinear material properties. 

Once these improvements to the model have been made, other improvements might 
be desirable. However, at this time it is not useful to speculate on what 
further improvements would be the most beneficial. The purpose of the improved 
models is really to mathematically determine what happens as seismic motion, 
partitioned into various combinations of P- , SV-, and SH-waves , approaches the 
ground surface at various angles of incidence. By comparing the results of 
such parametric studies to actual observed motion, it should be possible to 
begin to develop a better understanding of how and why motion varies with 
depth. In addition, the development of improved models would contribute to the 
construction of a definitive predictive model suitable for all situations. 

SEISMIC ANALYSIS AND DESIGN OF UNDERGROUND STRUCTURES 

This study indicates that there is a lack of appropriate analytical techniques 
for the determination of seismic stresses around tunnels and other large under- 
ground structures of arbitrary shape and for real geologic media. Existing 
dynamic codes are limited in their ability to model such important rock mass 
properties as joint slip, strain, softening, and dilatation. They are also 
somewhat limited in their ability to consider simultaneous propagation of 
different types of body waves (e.g., P-waves and SV-waves) with arbitrary angles 
of incidence. The importance of having such analytical techniques lies mostly 
in being able to conduct parametric studies of alternative locations and shapes 
of an opening for increased stability during seismic motion. Once such models 
are perfected, they will be useful in decisions regarding details of the support 
for specific designs. 

At this time, the development of analytical techniques to predict shaking damage 
to underground openings in rock is probably more important to the design of large 

- 197 - 



caverns than to the design of transportation or water tunnels. Little is known 
about the seismic stability of large caverns because there have been so few 
observations of large caverns during strong ground motion. In contrast, obser- 
vations of tunnels during earthquakes have been much more frequent and generally 
indicate the excellent stability of tunnels in hard, competent rock. Analytical 
techniques would be useful in resolving the uncertainty about cavern stability. 
In particular, analytical techniques would assist in assessing the effect of 
rock block sizes on the seismic stability of caverns. The sizes of rock blocks 
are generally more important to cavern stability than to tunnel stability because 
the block sizes are usually small compared with the cavern dimensions whereas 
they are large compared with the typical tunnel dimensions. A program to develop 
computer codes for stability evaluations for openings in rock, particularly for 
large caverns, is recommended below (Research Activity 7). 

This study also indicates that there is a general lack of procedures upon which 
to base design decisions regarding additional support requirements for soil and 
rock tunnels and for rock caverns (see Chapter 7). There is a need to further 
develop the empirical seismic design method so that it can be used in conjunc- 
tion with the fairly we 1 1 -developed empirical methods for static design. At 
this time, there is no clear correlation between incremental increases in the 
severity of the earthquake shaking and corresponding incremental increases in 
the support requirements. Two programs (Research Activities 8 and 9) are 
recommended to begin to clarify this correlation. 

Research Activity 7: Development of Computer Codes for 
Stability Evaluation of Openings in Rock 

The development of computer codes for the analysis of the stability of openings 
in rock with particular application to large caverns should be encouraged. The 
code might build upon the existing works in finite-element, finite-difference, 
discrete-element, and boundary-element methods. In particular, the development 
should focus on incorporating better models of the rock mass and its properties, 
such as joint slip, strain softening, and dilatation. Advances in the codes 
for dynamic analysis should be compatible with developments of these codes for 
static and thermal analysis. 



- 198 - 



Research Activity 8: Development of Empirical Procedures 
for Seismic Design 

The data base collected from studies of past and future earthquakes (Research 
Activities 1, 2, and 3) together with the records gathered from instrumented 
tunnels (Research Activity 5) should be carefully evaluated to develop 
empirical procedures for seismic design decisions. Tunnels might be grouped 
by different types and conditions of rock or soil so that variations in the 
support system for given ground conditions can be investigated. Then, by 
analyzing correlations between level of damage (or lack of damage) and various 
parameters representing the severity of the ground motion, it should be possible 
to draw conclusions about the additional needs for support for different ground 
conditions. The success of this proposed investigation requires a much larger 
and detailed data base than is presently available and is, therefore, dependent 
upon the careful execution of Research Activities 1, 2, 3, and 5- 

Research Activity 9: Analytical Parametric Study of 
Seismic Stability of Openings in Rock 

In conjunction with the development of a strictly empirical approach to seismic 
design decisions as described above, an analytical parametric study would be 
very useful in understanding those features of the rock mass and the support 
system that most affect the stability of an opening. An analytical parametric 
study could investigate the optimal use of rock bolts, shotcrete, steel sets, 
and various details of the support to stabilize openings in rock with different 
material properties, joint spacings, and joint orientations and under different 
magnitudes of in situ stress. The earthquake motion should be represented by 
two components of motion, which would be a much more realistic characterization 
than a single component of motion. 

The success of Research Activity 9 wi 1 1 depend upon the further development 
of analytical technologies as suggested in Research Activity 8. Verification 
of its findings will depend upon the detailed collection of data from past 
and future earthquakes (Research Activities 1, 2, and 3). 



- 199 - 



Appendix A 

Persons Contacted About Seismic Design off Underground Structures 

A number of persons in both private firms and government agencies were con- 
tacted and asked to voice their concerns about the seismic stability of under- 
ground structures and to outline their approaches to seismic design. A list 
of these persons is provided below. 



Agency or Fi rm 

Fenix & Scisson, Inc. 
Tulsa, Oklahoma 

Acres American Inc. 
Buffalo, New York 

McCarthy Engineering/ 
Construction, Inc. 
Tulsa, Oklahoma 

RE/SPEC Inc. 

Rapid City, South Dakota 

Bureau of Reclamation 
Denver, Colorado 

Harza Engineering 
Chicago, 1 1 1 inois 

California State Department 

of Water Resources 
Sacramento, California 

Foundation Sciences 
Portland, Oregon 

Parsons Brinckerhoff Quade 

& Douglas 
New York, New York, and 
San Francisco, California 

U.S. Army Corps of Engineers, 

Los Angeles District 
Los Angeles, California 

U.S. Department of Defense, 

Nevada Test Site 
Mercury, Nevada 



Person(s) 
R. S. Mayfield 



Dougal R. McCreath 



D. F. McCarthy 



Paul Gnirk 



Jim Warden 
J. S. Dodd 

Kolden Zerneke 
Wi 1 1 iam Shi eh 

Jack Marlette 



Larry Wi lkenson 
Ken Dodds 

T. R. Kuesel 
Elwyn King 
George Murphy 



Peter J. Hradilek 



Joe La Comb 



- 200 - 



Agency or Firm 



Person (s) 



U.S. Navy Public Works Center 
Great Lakes, Illinois 

J. Barry Cooke Inc. 
San Rafael, California 

University of Illinois 
Urbana, 1 1 1 i nois 

University of California, 

Berkeley 
Berkeley, California 



Lloyd C. Jones 

(now at Purdue University) 

J. Barry Cooke 



William J. Hall 



Tor L. Brekke 
Richard Goodman 



Merritt Cases 

Red lands, California 



J. L. Merritt 



TeraTek 

Salt Lake City, Utah 

Agbabian Associates 
El Segundo, California 



Howard R. Pratt 



George Young 
Bob Ewing 



Jacobs Associates 

San Francisco, California 

Northwestern University 
Evanston, 1 1 1 inois 



J. Donovan Jacobs 

A. M. (Pete) Petrofsky 

Theodore Belytschko 



Massachusetts Institute of 

Technology 
Cambridge, Massachusetts 

San Francisco Department of 

Publ ic Works 
San Francisco, California 



Herbert Einstein 



Frank Moss 
W. J. Scruggs 
Stephen Soo 



San Francisco Water 

Department 
San Francisco, California 



Paul Matsumura 



East Bay Municipal Utility 

District 
Oakland, California 

National Science Foundation 
Washington, D.C. 



Walter Anton 



William W. Hakala 



Federal Highway Administration 
Washington, D.C. 



James D. Cooper 



- 201 - 



Agency or Fi rm 

Marin Historical Society 
San Rafael, California 

University of Arizona 
Tucson, Arizona 

Southern Pacific 

Transportation Co. 
San Francisco, California 

Ontario Hydro 
Toronto, Ontario 

Golder Associates 
Vancouver, British Columbia 

Norwegian Geotechnical 

Insti tute 
Oslo, Norway 

Hagconsult AB 
Stockholm, Sweden 

The Royal Institute of 

Technology 
Stockholm, Sweden 

Norwegian Institute of 

Technology 
Trondheim, Norway 

VBB Engineers 
Stockholm, Sweden 

Basler & Hofmann 
Zurich, Switzerland 

Electric Power Development 

Company 
Tokyo, Japan 

Muto Institute of Structural 

Mechanics, Inc. 
Tokyo, Japan 

Japan Railway Construction 

Public Corporation 
Tokyo, Japan 



Person(s) 
L. Mazzini 

Charles E. Glass 



Tom L. Ful ler 
Lynn Farrar 



R. C. Oberth 
Evert Hoek 
Nicholas Barton 

C. 0. Morfeldt 
Bengt B. Broms 

Einar Broch 

Rainer Massarsch 
R. Sagesser 
Y. Ichikawa 



K. Muto 
K. Uchida 



T. Ohira 
T. Tottori 
K. Aoki 



- 202 - 



Agency or Fi rm Person(s) 

Research Laboratory, Schmizu 

Construction Co. 
Tokyo, Japan 

Public Works Research 

I nsti tute 
Tsukuba, Japan 



K. 


Yamahara 


K. 


Fukumi tsu 


E. 


Kuribayashi 


T. 


Iwasaki 


T. 


Tazaki 


T. 


Konda 


K. 


Kawashima 



- 203 - 



Appendix B 

Abridged Modified Mercalli Intensity Scale 

Descriptions of intensity values I through XII of the abridged Modified Mercall 
Intensity scale 2 are given below. 

I. Not felt except by a very few under especially favor- 
able circumstances. (I Rossi-Forel scale.) 

II. Felt only by a few persons at rest, especially on 

upper floors of buildings. Delicately suspended ob- 
jects may swing. (i to II Rossi-Forel scale.) 

III. Felt quite noticeably indoors, especially on upper 

floors of buildings, but many people do not recognize 
it as an earthquake. Standing motorcars may rock 
slightly. Vibration like passing of truck. Duration 
estimated. (ill Rossi-Forel scale.) 

IV. During the day felt indoors by many, outdoors by few. 
At night, some awakened. Dishes, windows, doors dis- 
turbed; walls make creaking sound. Sensation like 
heavy truck striking building. Standing motorcars 
rocked noticeably. (IV to V Rossi-Forel scale.) 

V. Felt by nearly everyone, many awakened. Some dishes, 
windows, and so on broken; cracked plaster in a few 
places; unstable objects overturned. Disturbances 
of trees, poles, and other tall objects sometimes 
noticed. Pendulum clocks may stop. (V to VI Rossi- 
Forel scale.) 

VI. Felt by all, many frightened and run outdoors. Some 
heavy furniture moved; a few instances of fallen 
plaster and damaged chimneys. Damage slight. (VI 
to VII Rossi-Forel scale.) 

VII. Everybody runs outdoors. Damage negligible in build- 
ings of good design and construction; slight to moder- 
ate in well-built ordinary structures; considerable 
in poorly built or badly designed structures; some 
chimneys broken. Noticed by persons driving cars. 
(VIII Rossi-Forel scale.) 

VIII. Damage slight in specially designed structures; con- 
siderable in ordinary substantial buildings, with 
partial collapse; great in poorly built structures. 
Panel walls thrown out of frame structures. Fall of 
chimneys, factory stacks, columns, monuments, walls. 
Heavy furniture overturned. Sand and mud ejected in 
small amounts. Changes in well water. Persons driv- 
ing cars disturbed. (VIII+ to IX Rossi-Forel scale.) 



- 20h - 



IX. Damage considerable in specially designed structures; 
well-designed frame structures thrown out of plumb; 
great in substantial buildings, with partial collapse, 
Buildings shifted off foundations. Ground cracked 
conspicuously. Underground pipes broken. (IX+ Rossi- 
Forel scale.) 

X. Some well-built wooden structures destroyed; most 
masonry and frame structures destroyed with founda- 
tions; ground badly cracked. Rails bent. Landslides 
considerable from river banks and steep slopes. 
Shifted sand and mud. Water splashed, slopped over 
banks. (X Rossi-Forel scale.) 

XI. Few, if any, (masonry) structures remain standing. 

Bridges destroyed. Broad fissures in ground. Under- 
ground pipelines completely out of service. Earth 
slumps and land slips in soft ground. Rails bent 
greatly. 

XII. Damage total. Waves seen on ground surface. Lines 
of sight and level distorted. Objects thrown into 
the air. 



- 205 - 



Appendix C 

Summary of Damage to Underground Structures from Earthquake Shaking 

Information concerning damage to underground structures from earthquake 
shaking is summarized in tabular form in the pages that follow. One hundred 
and twenty-seven cases are cited. Each case has been assigned a number, 
which is shown in Column 1. The remaining columns (2 through 15) provide 
the following information, when available: 

Source of Data : Column 2 identifies the reference (s) from which 
the information in the following columns is obtained. 

Earthquake Data : Column 3 provides general information about the 
earthquake, such as location or name, date of occurrence, magni- 
tude (M) , and duration (D) . 

Underground Structure : Column k identifies the underground struc- 
ture by name or describes the type of structure if a name is not 
available. The distance of the structure from the earthquake 
epicenter (R) is also given. 

Underground Structure Data : Columns 5 through 8 provide informa- 
tion about the underground structure. The cross-sectional dimen- 
sions and depth of the structure are given in Columns 5 and 6, re- 
spectively. Column 7 describes the ground conditions, and Column 
8 indicates the type of support or lining used for the structure. 

Surface Shaking Data : Columns 9 through 12 provide information 
about the ground motion at the surface near the underground struc- 
ture. The effects of the earthquake on surface structures, etc., 
are given in Column 9- Column 10 lists the ground motion para- 
meters -- acceleration (a), velocity (v) , and displacement (d). 
Personal perceptions of surface ground motion are noted in Column 
11, and the intensity of the earthquake at the surface, estimated 
according to the Modified Mercalli Intensity (MM I) scale or the 
Rossi- Fore 1 scale, is given in Column 12. 



- 206 - 



Subsurface Shaking Data : Columns 13, 1^, and 15 provide infor- 
mation about the subsurface ground motion. The effects of the 
earthquake on the underground structure are given in Column 13. 
Personal perceptions of subsurface ground motion are noted in 
Column 14. Column 15 gives the intensity of the earthquake (MM I 
or Rossi-Forel) below the ground surface. 



- 207 - 



SUMMARY OF DAMAGE TO UNDERGROUND STRUCTURES 
FROM EARTHQUAKE SHAKING 



Num- 
ber 
(1) 


Source 

of Data 

(2) 


Earthquake 
Data 
(3) 


Underground 
Structure 
(4) 


Underground 


Structure Data 






Cross 
Section 

(5) 


Depth 
(6) 


Ground 

Conditions 

(7) 


Support, 
Lining 

(8) ' 


1 


15, 17, 

19, 24 


San Francisco, 

Cal ifornia 

1906 

M = 8.3, 

D = 40 sec 


Wright 
Tunnel #2 

near 
Los Gatos 
R = 135.8 km 


4.0 m wide 


206 m 


sandstone, 
jasper 


timber 
sets 




2 


15, 17, 
19, 24 


M 


Wright 

Tunnel #1 

R = 135 km 


4.0 m wide 


214 m 


shale, 

serpentine, 

soapstone 


timber 
sets 




3 


15, 17, 
24 


Kwanto (Kanto) 

Region, 1923, 

or 

Great Tokyo, 

1923 

M = 8.16, 

D = 5b sec 


Terao 
R = 31.6 km 








bricks 




4 


15, 17, 
24 


" 


Hichigama 
R = 36.4 km 












5 


15, 17, 
24 


" 


Taura 
R = 31.6 km 




15 m 


loose 

surface 

rock 






6 


15, 17, 
24 




Numama 
R = 46.0 km 












7 


15, 17, 
24 


" 


Nokogiri- 

Yama 
R = 70.7 km 








concrete 




3 


15, 17, 
24 


ll 


Kanome- 

Yama 

R = 26.9 km 






boulders in 
slope 






9 


15, 17, 
24 


il 


Ajo 
R = 25.0 km 













- 208 - 



Surface Shaking Data 


Subsurface Shaking Data 


Surface 

Effects 

(9) 


Ground Motion 

Parameters 

(10) 


Personal 

Perceptions 

(ID 


Intensity 

(12) 


Underground 
Effects 
(13) 


Personal 
Perceptions 
(14) 


Estimated 
Intensity 
(15) 


80% of chim- 
neys damaged, 
nearly all 
brick fronts 
cracked, a 
dozen upheav- 
als of side- 
walks (in Los 
Gatos) 


a = 0.13g 

v = 26.8 cm/ sec 

d = 41.9 cm 




IX to X 
Rossi - 
Forel 


timbers broken, 
roof caved 






■I 


a = 0.13g 

v = 26.9 cm/sec 

d = 42.1 cm 

a = 0.47g 

v = 82.5 cm/sec 

d = 91.8 cm 

a = 0.42g 

v = 74.8 cm/sec 

d = 99.1 cm 

a = 0.47g 

v = 82.5 cm/sec 

d = 91.8 cm 

a = 0.35g 

v = 62.8 cm/sec 

d = 75.1 cm 

a = 0.24g 

v = 43.9 cm/sec 

d = 57.7 cm 

a = 0.52g 

v = 91.6 cm/sec 

d = 117.1 cm 

a = 0.55g 

v = 95.8 cm/sec 

d = 112.5 cm 




■I 


timbers broken, 
roof caved, 
(also damage 
due to fault- 
ing) 

cracked brick 
portal , no 
interior dam- 
age 

no damage 

no damage 

cracked brick 
portal , no 
interior dam- 
age 

concrete walls 
slightly frac- 
tured, some 
spalling of 
concrete 

no interior 
damage (masonry 
portal damaged 
by landslide) 

n 







(continued) 



- 209 - 



SUMMARY OF DAMAGE TO UNDERGROUND STRUCTURES 
FROM EARTHQUAKE SHAKING (Continued) 



Num- 
ber 
(1) 


Source 

of Data 

(2) 


Earthquake 
Data 
(3) 


Underground 
Structure 
(4) 


Underground 


Structure Data 






Cross 
Section 

(5) 


Depth 
(6) 


Ground 

Conditions 

(7) 


Support, 

Lining 

(8) 


10 


15, 17, 
24 


Kwanto (Kanto) 
Region, 1923, 

or 

Great Tokyo, 

1923 

M = 8.16, 

D = 35 sec 


Ippamatzu 
R = 25.0 km 








masonry 




11 


15, 17, 
24 


u 


Nagoye 
R = 24.0 km 




30 m 








12 


15, 17, 
24 


ii 


Komine 
R = 26.9 km 




1.5-6 m 




rein- 
forced 
concrete 




13 


15, 17, 
24 


» 


Fudu San 
R = 24.0 km 




18 m 


thin, loose 
material on 
hillside 






14 


15, 17, 
24 


ii 


Meno- 
Kamiama 
= 32.0 km 




16.5 m 


loose rock 


masonry 




15 


15, 17, 
24 


II 


Yonegami- 

Yama 
R = 32.0 km 




50 m 




masonry 




16 


15, 17, 
24 


" 


Shimomaki- 

Matsu 

R = 36.5 km 




29 m 




masonry 




17 


15, 17, 
24 


II 


Happon-Matzu 
R = 20.0 km 




20 m 


loose 

material on 
steep slope 






18 


15, 17, 
24 


ii 


Nagasaha- 

Yama 

R = 20.0 km 




90 m 




brick 

and 

concrete 




19 


15, 17, 
24 


M 


Hakone 

No. 1 

R = 15.6 km 




61 m 








20 


15, 17, 
24 


II 


Hakone 

No. 2 

R = 15.6 km 













- 210 - 



Surface Shaking Data 


Subsurface Shaking Data 


Surface 

Effects 

(9) 


Ground Motion 

Parameters 

(10) 


Personal 

Perceptions 

(11) 


Intensity 
(12) 


Underground 

Effects 

(13) 


Personal 

Perceptions 

(14) 


Estimated 
Intensity 
(15) 




a = 0.55g 

v = 95.8 cm/sec 

d = 112.5 cm 

a = 0.50g 

v = 98.1 cm/sec 

d = 107.4 cm 

a = 0.52g 

v =91.6 cm/sec 

d = 99.1 cm 

a = 0.50g 

v = 98.1 cm/sec 

d = 107.4 cm 

a = 0.46g 

v = 81.8 cm/sec 

d = 91.2 cm 

a = 0.46g 

v = 81 .8 cm/sec 

d = 91.2 cm 

a = 0.42g 

v = 74.7 cm/sec 

d = 85.3 cm 

a = 0.63g 

v = 108.7 cm/ sec 

d = 112.5 cm 

a = 0.59g 

v = 102.1 cm/sec 

d = 107.4 cm 

a = 0.72g 

v = 123.0 cm/sec 

d = 123.2 cm 

a = 0.72g 

v = 123.1 cm/sec 

d = 123.2 cm 






masonry dis- 
lodged near 
floor 

interior 
cracked 

destroyed, 
ceiling slabs 
caved in, 
formed section 
cracked 

cracked masonry 
portal , no in- 
terior damage 

partial 
collapse 

minor interior 
masonry damage, 
cracks near 
portal 

deformed inte- 
rior masonry 

badly cracked 
interior 

some interior 
fractures in 
bricks and 
concrete 

interior cracks 
no damage 






i 















(continued) 



- 211 - 



SUMMARY OF DAMAGE TO UNDERGROUND STRUCTURES 
FROM EARTHQUAKE SHAKING (Continued) 



Num- 
ber 
(1) 



Source 

of Data 

(2) 



Earthquake 
Data 
(3) 



Underground 

Structure 

(4) 



Underground Structure Data 



Cross 

Section 

(5) 



Depth 
(6) 



Ground 

Conditions 

(7) 



Support, 

Lining 

(8) ' 



21 



22 



23 



24 



25 



26 



27 



28 



29 



15, 17, 
24 



15, 17, 

24 



15, 17, 
24 



15, 
24 


17, 


15, 
24 


17, 


15, 
24 


17, 



15, 17, 
24 



15, 17, 
24 



15, 17, 
24 



Kwanto (Kan to) 
Region, 1923, 

or 

Great Tokyo, 

1923 

M = 8.16, 

D = 35 sec 



Idu Peninsula 

1930 

M = 7.0 

D = 15 sec 



Fukui 
1948 



Hakone 

No. 3 

R = 17.2 km 



Hakone 

No. 4 

R = 19.7 km 

Hakone 

No. 7 

R = 22.4 km 



Yose 
26.9 km 



Doki 
R = 61.0 km 



Namuya 
R = 63.0 km 



Mineoka- 

Yama 

R = 65.0 km 



Tanna 
R = 0.0 km 



Kumasaka 
R = 25.0 km 



46 m 



49 m 



31 m 



20 m 



very 
shallow 



75 m 



150 m 



fissured, 
faulted, 
weathered 
rock 

soft, fine- 
grain rock 



some 

basalt, de- 
formed rock 



agglomerate 

and 

andesite 



brick 



brick 

and 

concrete 



masonry 



concrete 



brick 



212 



Surface Shaking Data 


Subsurfa 


:e Shaking Data 


Surface 

Effects 

(9) 


Ground Motion 

Parameters 

(10) 


Personal 

Perceptions 

(11) 


Intensity 
(12) 


Underground 

Effects 

(13) 


Personal 

Perceptions 

(14) 


Estimated 
Intensity 

(15) 




a = 0.69g 

v = 117.4 cm/sec 

d = 119.0 cm 






interior 
cracks, ceiling 
collapse near 
portal , some 
damage to 
masonry portal 








a = 0.64g 

v = 109.6 cm/sec 

d = 113.1 cm 






collapse of 
loose material 








a = 0.59g 

v = 102.1 cm/sec 

d = 107.4 cm 






interior col- 
lapse 








a = 0.52g 

v = 91.6 cm/sec 

d = 99.1 cm 






shallow por- 
tions col- 
lapsed and 
dayl ighted 








a = 0.27g 

v = 49.9 cm/sec 

d = 63.4 cm 






collapsed at 
shallow parts 








a = 0.26g 

v = 48.5 cm/sec 

d = 62.1 cm 






cave-in, cracks 
with 25-cm dis- 
placement, pos- 
sibly due to 
landsl iding 








a = 0.26g 

v = 47.3 cm/sec 

d = 60.9 cm 






cracks in 
bulges in 
masonry from 
local earth 
pressure 






over tunnel , 
55% of dwell- 
ings de- 
stroyed, sur- 
face fault 
displacements 
for 15 km 


a = 0.30g 

v = 39.5 cm/sec 

d = 39.3 cm 






few cracks in 
walls (major 
damage due to 
faulting) 

no interior 
damage, brick 
arches of 
portal par- 
tially frac- 
tured 







(continued) 



- 213 - 



SUMMARY OF DAMAGE TO UNDERGROUND STRUCTURES 
FROM EARTHQUAKE SHAKING (Continued) 



Num- 
ber 
(1) 


Source 

of Data 

(2) 


Earthquake 
Data 
(3) 


Underground 
Structure 

(4) 


Underground 


Structure Data 




Cross 

Section 

(5) 


Depth 
(6) 


Ground 

Conditions 

(7) 


Support, 
Lining 

(8) " 


30 


15, 17, 
24 


Hokkaido 

(off Tokachi ) 

1952 

M = 8.0 
D = 30-35 sec 










concrete 
brick 


31 


15, 17, 
21, 22, 
24 


Kern County 

1952 

M = 7.7 


S. Pacific 

R.R. 

Tunnel #3 

R = 46.0 km 




46 m 


decomposed 
diori te 
(granite) 


timber 
and 

30-53 cm 
concrete 


32 


15, 17, 
21, 22, 

24 


II 


S.P.R.R. 

#4 
R = 46.0 km 




38 m 


decomposed 
diori te, 
many sur- 
face cracks 


it 


33 


15, 17, 
21, 22, 
24 


ii 


S.P.R.R. 
#5 
R = 46.5 km 




76 m 


n 


ii 


34 


15, 17, 
21, 22, 
.24 


II 


S.P.R.R. 

#6 
R = 46.5 km 




15 m 


decomposed 
diorite 


ii 


35 


17, 24 


Kita Mi no 

1961 

M = 7.2 

D = 15-20 sec 


Powerhouse 
R = 32.0 km 


77 m long, 
22 m wide, 
43 m high 




jointed, 

igneous 

rock 




36 


17, 24 


ii 


Aqueduct 






soft ground 




37 


17, 24 


Niigata, 1964 

M = 7.5 
D = 20-25 sec 


Nezugaseki 










38 


17, 24 




Terasaka 











- 2\k - 



Surface Shaking Data 


Subsurface Shaking Dat 


i 


Surface 

Effects 

(9) 


Ground Motion 
Parameters 

(10) 


Personal 

Perceptions 

(11) 


Intensity 
(12) 


Underground 

Effects 

(13) 


Personal 

Perceptions 

(14) 


Estimated 

Intensity 

(15) 








IV to V 
MM I 


minor cracking 
in both brick 
and concrete 
linings 








a = 0.24g 

v = 37.5 cm/sec 

d = 42.9 cm 




XI MMI 


no interior 
damage due to 
shaking reported 
(severely dam- 
aged by fault- 
ing) 








a = 0.24g 

v = 37.5 cm/sec 

d = 42.9 cm 






ii 








a = 0.24g 

v = 37.2 cm/sec 

d = 42.7 cm 






it 


> 






a = 0.24g 

v = 37.2 cm/sec 

d = 42.7 cm 






no interior 
damage due to 
shaking re- 
ported (frac- 
tured due to 
fault movement) 








a = 0.25g 

v = 33.7 cm/ sec 

d = 39.3 cm 






no damage 








M 






cracking 

spalling of 
concrete at 
crown, cracking 
at portal 

spall ing of 
concrete at 
crown, crushing 
of invert at 
bottom of side- 
wal Is 







(continued) 



- 215 - 



SUMMARY OF DAMAGE TO UNDERGROUND STRUCTURES 
FROM EARTHQUAKE SHAKING (Continued) 



Num- 
ber 
(1) 


Source 

of Data 

(2) 


Earthquake 
Data 
(3) 


Underground 

Structure 

(4) 


Un 


derground Structure Data 




Cross 

Section 

(5) 


Depth 
(6) 


Ground 

Conditions 

(7) 


Support, 
Lining 

(8) " 


39 


17, 23, 
24 


Great Alaska 
1964 
M = 8.4 
D = 45 sec 


Whittier 1 
R = 75.0 km 






greywacke 


unlined, 

except 

for 

wooden 

shoring 

at 

portals 


40 


17, 23/ 
24 


il 


Whittier 2 
R = 75.0 km 








ll 


41 


17, 23, 
24 


" 


Seward 1 
R = 85.0 km 








li 


42 


17, 23, 
24 


il 


Seward 2 
R = 85.0 km 








II 


43 


17, 23, 

24 


" 


Seward 3 

R = 100 km 










44 


17, 23, 
24 


II 


Seward 4 
R = 100 km 








II 


45 


17, 23, 
24 


il 


Seward 5 
R = 110 km 








" 


46 


17, 23, 
24 


" 


Seward 6 
R = 115 km 








ll 


47 


17, 24, 
27 


San Fernando 

1971 

M = 6.4 

D = 15 sec 


Balboa Inlet 
R = 16.0 km 


4.3 m 
diameter 


shallow, 

under 

canyon 




re i n - 

forced 

concrete 


48 


17, 24, 
27 




San Fernando 
R = 16.0 km 


5.5 m 
diameter 


approx. 
46 m 


all uvi urn- 
soft, satu- 
rated silt, 
sand, and 
gravel 


rain- 
forced 
concrete, 
under 
construc- 
tion 


49 


17, 24, 
27 


ii 


Mac lay 
R = 16.0 km 


2.0 m high, 

horseshoe 

shaped 






concrete 


50 


17, 24, 
27, 28 


" 


Chatsworth 

R = 20.0 km 


2.0 in 
diameter 






concrete 



- 216 - 





Surface Shakinc 


1 Data 




Subsurface Shaking Data 


Surface 

Effects 

(9) 


Ground Motion 

Parameters 

(10) 


Personal 

Perceptions 

(ID 


Intensity 
(12) 


Underground 

Effects 

(13) 


Personal 

Perceptions 

(14) 


Estimated 

Intensity 

(15) 




a = 0.26g 

v = 52.0 cm/sec 

d = 79.4 cm 




IX to XI 
MMI 


overhead ravel- 
ling of materi- 
al which fell 
on track 








a = 0.26g 

v = 52.0 cm/sec 

d = 79.4 cm 




il 


no damage 








a = 0.23g 

v = 46.3 cm/sec 

d = 64.8 cm 




ii 


no damage 








a = 0.23g 

v = 46.3 cm/sec 

d = 64.8 cm 




It 


,io damage 








a = 0.19g 

v = 39.7 cm/sec 

d = 60.9 cm 




II 


no damage 








II 




" 


no damage 








a = 0.19g 

v = 36.2 cm/sec 

d = 56.7 cm 




II 


no damage 








a = 0.17g 

v = 34.7 cm/ sec 

d = 56.7 cm 




II 


no damage 








a = 0.23g 

v = 23.9 cm/sec 

d = 21.0 cm 




X MMI 


severe spall ing, 
steel 'oars de- 
formed, severity 
attributed to 








II 




X MMI 


canyon 

no damage due 
to shaking re- 
ported (damage 
dje to fault- 
ing) 








II 




X MMI 


wide, long 
cracks, but 
] iner did not 
fall into tun- 
nel 








a = 0.20g 

v = 21.4 cm/ sec 

d = 19.4 cm 




VIII MMI 


slight damage 







(continued) 



- 217 - 



SUMMARY OF DAMAGE TO UNDERGROUND STRUCTURES 
FROM EARTHQUAKE SHAKING (Continued) 



Num- 
ber 
(1) 


Source 

of Data 

(2) 


Earthquake 
Data 
(3) 


Underground 

Structure 

(4) 


Underground Structure Data 


Cross 

Section 

(5) 


Depth 
(6) 


Ground 

Condi tions 

(7) 


Support, 

Lining 

(8) " 


51 


17, 24, 
27 


San Fernando 

1971 

M = 6.4 

D = 15 sec 


Tehachapi 1 
R = 70.0 km 


7.2 m 
diameter 










52 


17, 24, 
27 


M 


Van Norman 
Inlet 
R = 33.0 km 












53 


17, 24, 
27 


ii 


Tehachapi 2 
R = 73.0 km 


7.2 m 
diameter 










54 


17, 24, 
27 


H 


Tehachapi 3 
R = 73.0 km 


7.2 m 
diameter 










55 


17, 24, 
27 


M 


Carley 

Porter 

R = 65.0 km 


6.1 m 
diameter 










56 


17, 24, 
27 


ii 


Van Morrison 

North 

(first 

Los Angeles 

aqueduct) 

R = 23.0 km 


2.9 m x 
3.2 m 






un rein- 
forced 
concrete 




57 


17, 24 


H 


Saugus 
R = 23.0 km 












58 


17, 24 


H 


San 
Francisquito 
R = 24.5 km 












59 


17, 24 


ii 


Elizabeth 
R = 27.3 km 












60 


17, 24 


ii 


Antelope 
R = 37.5 km 












61 


17, 24 


Inyo -Kern 

1946 

M = 6.3 

D = ? 


Jawbone 1 
R = 26.0 km 












62 


17, 24 




Jawbone 2 
R = 28.0 km 













- 218 - 







Surface Shakin 


g Data 




Subsurface Shaking Data 




Surface 

Effects 

(9) 


Ground Motion 

Parameters 

(10) 


Personal 

Perceptions 

(11) 


Intensity 
(12) 


Underground 

Effects 

(13) 


Personal 
Perceptions 

(14) 


Estimated 

Intensi ty 

(15) 






a = 0.07g 

v = 8.7 cm/sec 

d = 10.0 cm 




V MMI 


no damage 










a = 0.15g 

v = 15.8 cm/sec 

d = 15.5 cm 






no damage 










a = 0.07g 

v = 8.4 cm/sec 

d = 9.7 cm 




V MMI 

V MMI 


no damage 
no damage 










a = 0.08g 

v = 9. 3 cm/sec 

d = 10.5 cm 




V MMI 


no damage 










a = 0.19g 

v = 19.8 cm/sec 

d = 18.3 cm 




VIII to X 

MMI 


hundreds of new 
fractures in 
concrete lin- 
ing, up to 
6 mm, no struc- 
tural damage, 
fractures pri- 
marily circum- 
ferential , also 
longitudinal 
and diagonal 

no damage 










a = 0.18g 

v = 19.1 cm/sec 

d = 17.8 cm 






no damage 










a = 0.17g 

v = 17.9 cm/sec 

d = 17.0 cm 






no damage 










a = 0.13g 

v = 14.4 cm/sec 

d = 14.5 cm 






no damage 










a = 0.16g 

v = 16.8 cm/sec 

d = 15.7 cm 






no damage 










a = 0.16g 

v = 16.0 cm/sec 

d = 15.2 cm 






no damage 







(continued) 



- 219 - 



SUMMARY OF DAMAGE TO UNDERGROUND STRUCTURES 
FROM EARTHQUAKE SHAKING (Continued) 



Num- 
ber 
(1) 


Source 

of Data 

(2) 


Earthquake 
Data 
(3) 


Underqround 

Structure 

(4) 


Underground Structure Data 


Cross 

Section 

(5) 


Depth 
(6) 


Ground 

Conditions 

(7) 


Support, 

Lining 

(8) 


63 


17, 24 


Inyo-Kern 

1946 

M = 6.3 

D = ? 


Jawbone 3 
R = 31.0 km 










64 


17, 24 


■I 


Freeman 
R = 22.0 km 










65 


17, 24 


Arvin 

Tehachapi 

1952 

M = 7.7 

D = ? 


Saugus 
R = 90.0 km 










66 


17, 24 


M 


San 
Francisqui to 
R = 75.0 km 










67 


17, 24 


li 


Elizabeth 
R = 70.0 km 










68 


17, 24 


II 


Antelope 
R = 48.0 km 










69 


17, 24 


" 


Jawbone 
R = 90.0 km 










70 


17, 24 


Cholame, 1922 
M = 6.1 


Jawbone 
R = 52.0 km 










71 


17, 24 


'■ 


Freeman 
R = 52.0 km 










72 


15, 16 


Kern County 

1952 
Aftershock 
M = 6.6 or 6.1 
D = ? 


Crystal Cave 










73 


16 


Chile, 1960 


coal mines 
under ocean 










74 


15 


Montana 
June 27, 1925 


mines under 
Butte, 
Barker 




76 m 







- 220 - 





Surface Shakinc 


1 Data 


Subsurface Shaking Data 


Surface 
Effects 

(9) 


Ground Motion 

Parameters 

(10) 


Personal 

Perceptions 

(11) 


Intensity 
(12) 


Underground 

Effects 

(13) 


Personal 

Perceptions 

(14) 


Estimated 

Intensity 

(15) 




a = 0.14g 

v = 15.0 cm/sec 

d = 14.4 cm 






no damage 








a = 0.18g 

v = 18.5 cm/sec 

d = 16.9 cm 






no damage 








a = 0.14g 

v = 23.0 cm/sec 

d = 31.0 cm 






no damage 








a = 0.17g 

v = 27.2 cm/sec 

d = 35.0 cm 






no damage 








a = 0.18g 

v = 29.0 cm/ sec 

d = 36.7 cm 






no damage 








a = 0.25g 

v = 39.7 cm/sec 

d = 46.3 cm 






no damage 








a = 0.14g 

v = 23.0 cm/sec 

d = 31.0 cm 






no damage 








a = 0.08g 

v = 8.5 cm/sec 

d = 8.9 cm 






no damage 








n 


generally, 
quake was 
sharply 
felt 

generally 
noticed at 
surface 




no damage 
no damage 

no damage 


not noticed 
in cave 

miners 
heard 
strange 
noises 

generally 
unaware of 
earthquake 





(continued) 



- 221 - 



SUMMARY OF DAMAGE TO UNDERGROUND STRUCTURES 
FROM EARTHQUAKE SHAKING (Continued) 



1 


Source 

of Data 

(2) 


Earthquake 
Data 
(3) 


Underground 

Structure 

(4) 


Underground 


Structure Data 






Num- 
ber 

(1) 


Cross 
Section 

(5) 


Depth 
(6) 


Ground 

Conditions 

(7) 


Support, 

Lining 

(8) 


75 


15, 16 


Sonora, Mexico 
May 3, 1887 


mines at 
Tombstone 

and 
Bisbee, 
Arizona 




46 m 


limestone 
and other 
rocks 


some 
timber- 
ing 








ii 


ll 




152 m 


hard 
limestone 


ii 








ii 


ii 




152 m 


soft 
limestone 


ii 




76 


16 


Cedar Mt., 

Nevada 

December 21, 

1932 

M = 7.3 


various 
mines 


\ 










77 


16 


Excelsior 

Mts. , Nevada 

January 1, 

1930 

M = 6.3 


mine tunnel 
near Marietta 












78 


16 


ll 


Silver Dike 
Mine 












79 


16 


ll 


Qua i ley 
Mine 












80 


16 


Idaho 
May 9, 1944 


Korning 

Mine 

at Mullan 




1,350 m 








81 


16 


Calif. -Nev., 

Inyo-Mono 

counties 

August 24, 

1945 


Lone Pine 
Mine 













- 222 - 





Surface Shaki 


rig Data 




Subsurfa 


ce Shaking Data 




Surface 

Effects 

(9) 


Ground Motion 

Parameters 

(10) 


Personal 

Perceptions 

(11) 


Intensity 
(12) 


Underground 

Effects 

(13) 


Personal 

Perceptions 

(14) 


Estimated 
Intensity 
(15) 


falling 

plaster, 

chimneys, 

disarranged 

foundations, 

resetting 

of engines 








minor damage, 
rock fell from 
roof, making 
loud noises 


heavy roar- 
ing noise, 
vibration 
culminating 
with a jolt 




n 










miners 
frightened, 
lost 
equilibrium 




■1 










miners did 
not notice 
anything 
unusual 




a stone cabin 
denolished, a 
mine mill dam- 
aged consider- 
ably 




people at 
surface 
heard more 
noise and 
were 
frightened 

accutely 
perceptible 

felt by 
many 


IV to VI 

MM I 

VI MMI 
near 

Burke and 
Mullan 
towns 


some sloughing 
underground in 
various mines 

considerable 
damage 

timbers broken, 
a heading 
knocked out, 
staging fell , 
flying rock as 
timbers broke 


miners lost 
balance, 
heard less 
noise and 
were less 
frightened 
than people 
on the sur- 
face 

scarcely 
noticed 




windows rat- 
tled, no sur- 
face damage 










officials 
heard roar 
which 

drowned out 
blasting 





(continued) 



- 223 - 



SUMMARY OF DAMAGE TO UNDERGROUND STRUCTURES 
FROM EARTHQUAKE SHAKING (Continued) 



Num- 
ber 
(1) 


Source 

of Data 

(2) 


Earthquake 
Data 
(3) 


Underground 

Structure 

(4) 


Underground ! 


Structure Data 






Cross 

Section 

(5) 


Depth 
(6) 


Ground 

Conditions 

(7) 


Support, 

Lining 

(8) 


82 


16 


Inyo County, 

Cal ifornia, 

Owens Valley 

March 26, 1872 


Cerro Gordo 

and Eclipse 

Mine 












83 


16 


Sonora, 
Mexico 
May 3, 1887 
D = 20 sec 


mine at 

Tombstone, 

Arizona 


46 m and 
49 m 


46 m 
and 
183 m 








84 


16 


Reno, Nevada 

April 28, 1888 

D = 10 sec 


Orleans Mine 












85 


16 


■I 


Idaho Mine 




488 m 








86 


16 


Central 
California 
May 19, 1889 


Mayflower 

Mine in 
Forest Hill 




183 m 
and 
244 m 








87 


16 


Juab and 
Utah counties, 

Utah 
July 31, 1900 


Tintic Mine, 
Juab County 













- 224 - 





Surface Shakin 


g Data 




Subsurface Shaking Data 


Surface 


Ground Motion 


Personal 




Underground 


Personal 


Estimated 


Effects 


Parameters 


Perceptions 


Intensity 


Effects 


Perceptions 


Intensity 


(9) 


(10) 


(11) 


(12) 


(13) 


(14) 


(15) 


at Geyer 










rock motion 




Gulch, 70 or 










observed, 




80 km from 










especially 




Independence, 










in timber- 




Inyo County, 










ing, miners 




miners' cab- 










went to 




ins collapsed 










surface but 
soon re- 
turned to 
work 




no building 




load deto- 






miners at 




of any sta- 




nations, 






183 m felt 




bility dam- 




tremors for 






shock se- 




aged, no one 




1 minute 






verely and 




injured, RR 










some became 




track 11.5 cm 










sick, 




out of line 










miners at 




for 91 m 










46 m no- 




(see no. 75) 




washbowl 
rattled 
against a 
pitcher 
over mine 


VII MMI 
in Grass 
Valley 


mine flooded 


ticed shock 
less 

felt by 
miners 

not felt by 
miners 




at Coshen, 










miners came 




Utah County, 










to the sur- 




dishes were 










face 




broken, plas- 










frightened 




ter fell from 














walls, and a 














chimney was 














broken, at 














Santaquin, 














Utah County, 














an adobe 














house was 














split in two 














and people 














thrown from 














beds 















(continued) 



- 225 - 



SUMMARY OF DAMAGE TO UNDERGROUND STRUCTURES 
FROM EARTHQUAKE SHAKING (Continued) 



Num- 
ber 
(1) 


Source 

of Data 

(2) 


Earthquake 
Data 
(3) 


Underground 

Structure 

(4) 


Underground Structure Data 


Cross 

Section 

(5) 


Depth 
(6) 


Ground 

Conditions 

(7) 


Support, 

Lining 

(8) 


88 


16 


Juab and 
Utah counties, 

Utah 
July 31, 1900 


Mammouth 
Mine 












89 


16 


Kern County, 

California 

July 9, 1871 


Joe Walker 
Mine 












90 


16 


Humboldt 

County, 

California 

October 28, 

1909 

D = 30 sec 


Bully Hill 

Mine at 

Delamar, 

Cal ifornia, 

Shasta 

County 












91 


16 


Bishop, 

Inyo County, 

California 

March 21, 1917 


LADWP Tunnel 
under con- 
struction 













- 226 - 





Surface Shakin 


g Data 




Subsurfa 


:e Shaking Data 


Surface 


Ground Motion 


Personal 




Underground 


Personal 


Estimated 


Effects 


Parameters 


Perceptions 


Intensity 


Effects 


Perceptions 


Intensity 


(9) 


(10) 


(11) 


(12) 


(13) 


(14) 


(15) 


at Goshen, 








the deep shaft 






Utah County, 








was so twisted 






dishes were 








that the cage 






broken, plas- 








could not be 






ter fell from 








lowered to the 






walls, and a 








bottom 






chimney was 














broken, at 














Santaquin, 














Utah County, 














an adobe 














house was 














split in two 














and people 














thrown from 














beds 








mine almost in- 
stantly filled 
with water 


severe 
shock felt 
underground 




in Redding, 




3 sharp 






miners bad- 




clock in court- 




shocks 






ly fright- 




house stopped, 




felt, in 






ened by 




all chimneys 




Redding, 






rumbl ing 




and concrete 




persons oc- 






and shak- 




structures de- 




cupying up- 






ing, came 




stroyed at 




per floors 






to surface 




Rohnerville, at 




of brick 










Upper Mattole, 




buildings 










chimneys were 




rushed into 










destroyed and 




streets 










cemetary monu- 














ments were 














thrown down 














rock slides 




rapid 
trembling 
N-S for 25 
sec felt by 
many in 
Bishop 
area, 
felt at 
Crooked 
Creek Camp 
at the L.A. 
Power Bu- 
reau 39 km 
NW of Bishop 
for 30 sec 


IV MMI 

(at 

Bishop) 




shocks felt 
by workers 





(continued) 



- 227 - 



SUMMARY OF DAMAGE TO UNDERGROUND STRUCTURES 
FROM EARTHQUAKE SHAKING (Continued) 



Num- 
ber 
(1) 



Source 

of Data 

(2) 



Earthquake 
Data 
(3) 



Underground 

Structure 

(4) 



Underground Structure Data 



Cross 

Section 

(5) 



Depth 
(6) 



Ground 

Conditions 

(7) 



Support. 

Lining 

(8) 



92 



93 



16 



16 



94 



16 



95 



16 



96 



16 



Owens Valley, 

Inyo County, 

Cal i form' a 

September 4, 

1917 

Grass Valley, 
California 
November 7, 
1939 



Calumet, 

Michigan 

July 26, 1905 

(could have 

been induced 

seismici ty) 



Pleasant 

Valley, Nevada 

October 2, 

1915 

M = 7.75 



Idaho near 

Rathdrum 
November 27, 
1926 



Reward Gold 
Mine 



mine 



1,372 m 



mine 



mine 



Hecla Mine 



305 m 
and 
610 m 



- 228 - 





Surface Shakin 


9 Data 




Subsurfe 


ce Shaking Data 




Surface 


Ground Motion 


Personal 




Underground 


Personal 


Estimated 


Effects 


Parameters 


Perceptions 


Intensity 


Effects 


Perceptions 


Intensity 


(9) 


(10) 


(11) 


(12) 


(13) 


(14) 


(15) 






slight 


II MM I 




slight 








shock felt 






shock felt 
by one at 
rest 




doors flew 




noise like 






felt under- 




open, dishes 




an explo- 






ground 




fell off 




sion 










shelves, and 














bricks fell 














off chimneys 














in Grass 














Valley 














chimneys fell 




felt all 






sound like 




and plate 




over 






an explo- 




glass windows 




Keweenaw 






sion heard 




broke 




Peninsula, 
Michigan, 
felt heavi- 
est at 
Calumet, 
sound per- 
ceived as a 
loud explo- 
sion 






far down in 
the mine 




at Lovelock, 




at Kennedy, 


X MMI 


at Kennedy, 






large water 




there was a 


(at epi- 


concrete mine 






tanks were 




great roar 


center) 


foundations 






collapsed and 




and people 


V MMI 


cracked and 






cracks in 




were thrown 


(at Reno) 


mine tunnels 






road, great 




from their 




caved in 






increase in 




beds and 










water flow - 




others were 










new water 




thrown to 










rights filed, 




the floor 










new rift 














formed - ver- 














tical scarp 














1.5 to 4.5 m 














high, 35 km 














long 














slight damage 




strongly 






felt at 




at Kellogg 




felt at 
Wallace, 
vertical 
jar noted, 
two dis- 
tinct 

shocks felt 
at Rathdrum 






305 m but 
not at 
610 m 





(continued) 



- 229 - 



SUMMARY OF DAMAGE TO UNDERGROUND STRUCTURES 
FROM EARTHQUAKE SHAKING (Continued) 



Num- 
ber 
(1) 



Source 

of Data 

(2) 



Earthquake 

Data 

(3) 



Underground 

Structure 

(4) 



Underground Structure Data 



Cross 

Section 

(5) 



Depth 
(6) 



Ground 

Conditions 

(7) 



Support, 

Lining 

(8) " 



97 



16 



Wallace, Idaho 
December 18, 
1957 



Galena 
Silver Mine 



1,036 m 



98 



16 



Eastern 

Kentucky 

July 13, 1969 



Zinc Mine 

at Jefferson 

City 



99 



100 



101 



102 



30 



30 



30 



30 



Near Izu- 

Ohshima, Japan 

January 14, 

1978 

M = 7.0 



103 



30 



Tomoro 
Tunnel 



Izu-Ki tagawa 
Tunnel 



Izu-Atagawa 
Tunnel 



Izu-Inatori 



horseshoe 
shaped, 
other sec- 
tions are 
circular 



concrete 
1 ining 



assumed 
to be 
concrete 
lined 



steel 

sets 

encased 

in 

concrete 



Kawazu 



- 230 - 





Surface Shakin 


3 Data 


Subsurfa 


ce Shaking Date 


i 


Surface 


Ground Motion 


Personal 




Underground 


Personal 


Estimated 


Effects 


Parameters 


Perceptions 


Intensity 


Effects 


Perceptions 


Intensity 


(9) 


(10) 


(11) 


(12) 


(13) 


(14) 


(15) 






awakened 




extensive dam- 


frightened 








all and 




age, timber 


miners 








frightened 




fell and walls 


1,036 m 








many at 




caved in 


underground 








Wallace, 














also felt 














at Osburn 














and Mullan 










at Jefferson 








some rocks fell 






City, Tennes- 








in zinc mine 






see , a few 














bricks 














loosened on 














chimneys, at 














Knoxville, 














plaster and 














concrete 














cracked, 














houses shook 














strongly, and 














furni ture 














jumped up and 














down, plaster 














cracked at 














Seymour and 














small objects 














fell from 














shelves 








pieces of lin- 
ing in crown 
and sidewall 
fractured and 
fell out 

spalling of 
lining 

lining damaged, 
cause unknown 
to authors 






surface fault 








no damage due 






displacement 








to shaking re- 






of 46 cm, 








ported (exten- 






landslides, 








sive damage due 






minor damage 








to faulting) 






to buildings 








lining damaged, 
probably due to 
landsl iding 







(continued) 



231 - 



SUMMARY OF DAMAGE TO UNDERGROUND STRUCTURES 
FROM EARTHQUAKE SHAKING (Continued) 



Num- 
ber 
(1) 


Source 

of Data 

(2) 


Earthquake 
Data 
(3) 


Underground 

Structure 

(4) 




Underground 


Structure Data 




Cross 

Section 

(5) 


Depth 
(6) 


Ground 

Conditions 

(7) 


Support 

Lining 

(8) 


104 


30 


Near Izu- 

Ohshima, Japan 

January 14, 

1978 

M = 7.0 


Shi rata 
Tunnel 








rhyolite 


un re i n - 

forced 

concrete 

lining, 

some 

sections 

unlined 


105 


191 


Tangshan, 
China 
July 28,1978 
M = 8+ 


Tangshan 
Coal Mine 


shaft - 
12 m 
diameter 




40.5 m 






106 


191 


ii 


Lailuan 
Coal Mine 


several 
shafts 




700 m 







- 232 - 



Surface Shaking Data 


Subsurfa 


ce Shaking Data 


Surface 


Ground Motion 


Personal 




Underground 


Personal 


Estimated 


Effects 


Parameters 


Perceptions 


Intensity 


Effects 


Perceptions 


Intensity 


(9) 


(10) 


(11) 


(12) 


(13) 


(14) 


(15) 










many cracks 














throughout the 














lining, large 














landsl ide above 














the tunnel , a 














30.5-m lined 














section col- 














lapsed - proba- 














bly due to the 














landsl ide 






road surfaces 






XI MMI 


cross section 






fractured, 








fractured in 






subsidence, 








lower portion, 






cracking , 








shaft tilted 






sliding, and 








6°25' , mine 






differential 








flooded 






settling of 














road beds 














ii 






XI MMI 


ring fractures 
around the cy- 
linder walls 
in upper 20 m 
of several 
shafts, degree 
of shaft damage 
closely corre- , 
lated to soil 
conditions, 
serious damage 
where shaft 
passed through 
liquefied soil 
layer, 1.7 to 5 
times greater 
water flows 
into mines 







(continued) 



- 233 - 



SUMMARY OF DAMAGE TO UNDERGROUND STRUCTURES 
FROM EARTHQUAKE SHAKING (Continued) 



Num- 


Source 


Earthquake 


Underground 


Un 


derground 


Structure Data 






Cross 




Ground 


Support, 




ber 


of Data 


Data 


Structure 


Section 


Depth 


Conditions 


Lining 




(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


(8) 




107 


32 


Bishop, 


Pine Creek 


3-m x 3-m 


152 m 


hard, 


mostly 








California 


Tungsten 


drifts, 


to more 


strong, 


unsup- 








October 4, 


Mine about 


large rooms 


than 


competent 


ported, 








1978 


13 km from 


un to 24 m 


914 m 


granite, 


some 








M = 5.8 


epicenter 


x 6 m x 
6 m, 240 to 
320 km of 
tunnels 




quartzite, 
and marble, 
local pock- 
ets of de- 
composed, 
soft ground 


areas 
sup- 
ported 
with 
steel 
sets, 
timber, 
or rock 
bolts 
with 
wire 
mesh, 
shafts 
all sta- 
bilized 
with 
rock 
bolts 
and wire 
mesh 




108 


192 


II 


Helms Pumped 
Power Plant 

under 

construction 

R = 61 km 


large room 
under con- 
struction 


305 m 


granite 


rock 
bolts, 
spil- 
ing, 
shot- 
crete 




109 


193 


Gemoa-Friuli 

May 6, 1976 

M = 6.5 

D = 55 sec 


San Simeone 

highway 
tunnels (2), 

under 

construction 

in 

immediate 

epicentral 

region 


semi- 
circular or 
horseshoe, 
height = 
7. 6m 




limestone 


general- 
ly not 
lined 





- 23k - 



Surface Shaking Data 


Subsurface Shaking Data 


Surface 


Ground Motion 


Personal 




Underground 


Personal 


Estimated 


Effects 


Parameters 


Perceptions 


Intensity 


Effects 


Perceptions 


Intensity 


(9) 


(10) 


(11) 


(12) 


(13) 


(14) 


(15) 


cracks in 


a = 0.26g at 


people had 


V or VI 


no damage re- 


the motion 


III to IV 


masonry at 


Crowley Lake 


difficulty 


MM I 


ported, nothing 


was felt 


MMI 


foundations 


Dam, about 8 km 


standing, 




fell off 


underground 




of small 


from epicenter 


some became 




shelves, light 


at all 




houses, con- 


and 20 km from 


sick, loud 




fixtures swung 


depths, but 




tents of some 


mine 


rumbling, 




a couple of 


nobody expe- 




closets dis- 


a = 0.21g at 


booming, 




inches, one 


rienced dif- 




arranged, ob- 


LADWP Lower 


and crack- 




miner noticed 


ficulty 




jects like 


Gorge Power 


ing noises 




that the clear 


standing or 




vases fell 


House, about 


heard, peo- 




water turned 


became sick 




over, light 


16 km from epi- 


ple became 




milky colored 


or fright- 




fixtures 


center and 


frightened 




for 3 or 4 


ened, vari- 




swung, numer- 


16 km from mine 


and ran 




hours after 


ous levels 




ous rock 




outside 




quake, no in- 


of noise 




falls were 








crease in flow 


were re- 




reported on 








rates could be 


ported 




the slopes 








discerned 






and cliffs in 














the area, 














cracks re- 














ported in 














fills 














woodpi le col- 




felt in- 


IV to V 


no damage 


one or two 


II to III 


lapsed, rock 




doors by 


MMI 




impulses 


MMI 


falls on 




nearly ev- 






felt by 




slopes 




eryone and 
outdoors by 
most, many 
people ran 
outside, 
sensation 
of a heavy 
body strik- 
ing a 
building, 
windows and 
doors rat- 
tled and 
building 
frame 
creaked 






those away 
from work- 
ing head- 
ings, esti- 
mated dura- 
tion of one 
or two sec 




severe damage 


a = 0.34g ~15 




IX to X 


no damage 


workers 


VI MMI 


to or de- 


km from epi- 




MMI 


reported 


felt the 




struction of 


center 








quake, 




many build- 


v = 42 cm/sec 








abandoned 




ings 










their 
machinery 
and fled 





(continued) 



- 235 - 



SUMMARY OF DAMAGE TO UNDERGROUND STRUCTURES 
FROM EARTHQUAKE SHAKING (Continued) 



Num- 
ber 
(1) 


Source 

of Data 

(2) 


Earthquake 
Data 
(3) 


Underground 

Structure 

(4) 


Underground Structure Data 


Cross 

Section 

(5) 


Depth 
(6) 


Ground 
Conditions 
(7) 


Support, 

Lining 

(8) ' 


110 


194 


Gemoa-Friuli 

May 6, 1976 

M = 6.5 

D = 55 sec 


Foos Caves 










111 


31 


Miyagi- 

Ken-oki , Japan 

June 12, 1978 

M = 7.4 

D = 30 sec 


Hamadu 

Tunnel 

(near 

Matsushima) 

R = 160 km 


horseshoe 
shaped, 
6 m wi de 




tuff 


steel 
sets at 
portals, 
unrein- 
forced 
concrete 
lining 
in inte- 
rior 


112 


31 




Matsushima 
Tunnel 
(near 
Matsushima) 
R = 160 km 


horseshoe 
shaped , 
6 m wide 




ii 


unrein- 
forced 
concrete 
1 ined 


113 


31 


M 


3 other 

highway 

tunnels 

near 

Matsushima 


* 


* 


* 


* 


114 


20 


San Francisco, 

California 

1906 

M = 8.3, 

D = 40 sec 


S.P.R.R. 
San Francisco 

#1 
R = 45 km 


horseshoe 
shaped, 
9 m wide 


24 m 


Franciscan 

shale, 

weak, 

highly 

fractured 


under 
construc- 
tion, 
6-course 
brick 
1 ining 


lib 


20 


M 


S.P.R.R. 


two barrels, 


1.2-m 


loose soil 


6-course 








San Francisco 

#2 
R = 45 km 


each approx. 
6 ni wide 


cover 




brick 
lining, 
cut-and- 
cover 
construc- 
tion 


116 


20 


M 


S.P.R.R. 
San Francisco 

#3 
R = 46 km 


horseshoe 
shaped, 9 m 
wide 


46 m 


Franciscan 

shale, 

weak, 

highly 

fractured 


under 
construc- 
tion, 
6-course 
brick 
lining 


117 


20 


" 


S.P.R.R. 
San Francisco 
#4 
R = 47 km 


" 


38 m 


n 


ii 

















*Data similar to data for Nos. Ill and 112. 



- 236 - 





Surface Shaking Data 


Subsurface Shaking Data 




Surface 

Effects 

(9) 


Ground Motion 
Parameters 
(10) 


Personal 
Perceptions 
(11) 


Intensity 
(12) 


Underground 
Effects 
(13) 


Personal 
Perceptions 
(14) 


Estimated 
Intensity 
(15) 




severe damage 
to or de- 
struction of 
many buildings 


a = 0.34g ~15 
km from epi- 
center 
v = 42 cm/sec 




IX to X 
MM I 


no damage 
reported 








landslides, 
buildings dam- 
aged in the 
vicinity 








no damage 








ii 






VII 

Rossi- 

Forel 

VIII 
Rossi - 
Forel 

VII 

Rossi- 

Forel 

VII 

Rossi- 
Fore 1 


no damage 
no damage 

no damage 

both barrels 
collapsed 

no damage 
■I 







(continued) 



- 237 - 



SUMMARY OF DAMAGE TO UNDERGROUND STRUCTURES 
FROM EARTHQUAKE SHAKING (Continued) 



Num- 
ber 
(1) 


Source 

of Data 

(2) 


Ecrthquake 
Data 
(3) 


Underground 
Structure 
(4) 


Underground Structure Data 


Cross 
Section 

(5) 


Depth 
(6) 


Ground 

Conditions 

(7) 


Support, 

Lining 

(8) 


118 


20 


San Francisco, 

California 

1906 

M = 8.3, 

D = 40 sec 


S.P.R.R. 
San Francisco 
#5 
R = 50 km 


horseshoe 
shaped, 
9 m wide 




Franciscan 

shale, 

weak, 

highly 

fractured 


under 
construc- 
tion, 
6-course 
brick 
lining 


119 


195 


ii 


North 

Pacific 

Coast R.R., 

Bothin tunnel 

R = 11 km 










120 


195 


M 


North 

Pacific 

Coast R.R., 

Corte Madera 

tunnel 
R = 22 km 










121 
122 


27, 28 
27, 28 


San Fernando 

1971 

M = 6.4 

D = 15 sec 

n 


Maclay 

(Covered 

Conduit) 

R = 10.0 km 

Chatsworth 
(Covered 
Conduit) 

R = 20 km 


1.5 m high, 
1.8 m wide 

ii 


top 

probably 
at grade 

ii 


alluvium 
alluvium 


plain 
concrete 
sides and 
bottom, 
top slab 
rein- 
forced 
ii 


123 


27, 28, 
29 


ii 


Wilson Canyon 

Channel 
(Covered Box) 
R = 11 km 


3.7 m high, 
5.5 m wide, 
typical 


approx. 

1.5-m 

cover 




rein- 
forced 
concrete 


124 


27, 28, 
29 


■I 


Mansfield 

Street 

Channel 

(Covered Box) 

R = 11 km 


2.4 m high, 
2.4 m wide, 
typical 


approx. 

1.5-m 

cover 




rein- 
forced 
concrete 



- 238 - 





Surface Shakinc 


) Data 




Subsurface Shaking Data 


Surface 

Effects 

(9) 


Ground Motion 

Parameters 

(10) 


Personal 

Perceptions 

(11) 


Intensity 

(12) 


Underground 

Effects 

(13) 


Personal 

Perceptions 

(14) 


Estimated 

Intensity 

(15) 




(see No. 49; 
however, calcu- 
lations used 
R = 16 km in- 
stead of 10 km) 

(see No. 50) 

estimated hori- 
zontal accelera- 
tion 0.3-0.5g 

ii 




VII to 
VIII 
Rossi - 
Forel 

IX to X 
Rossi - 
Forel 

IX 

Rossi - 
Forel 

X MHI 

VIII MMI 
X MMI 

X MMI 


minor damage 
reported 

no report of 
damage 

ii 

heavy spall ing 
and long, wide 
cracks in sides 

some cracking 
and spall ing 

damage not 
attributed to 
shaking, but 
probably 
aggravated by 
cycling (se- 
vere damage 
due to fault- 
ing) 

ii 







(continued) 



- 239 - 



SUMMARY OF DAMAGE TO UNDERGROUND STRUCTURES 
FROM EARTHQUAKE SHAKING (Continued) 



Num- 


Source 


Earthquake 


Underground 


Underground ! 


Structure Data 




Cross 




Ground 


Support, 


ber 


of Data 


Data 


Structure 


Section 


Depth 


Conditions 


Lining 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


(8) 


125 


27 


San Fernando 


Bee Canyon 


triple-box, 




layers of 


rein- 






1971 


Storm Drain 


each 2.1m 




sandy silt 


forced 






M = 6.4 


R = 15 km 


high, 3.0 m 




and silty 


concrete 






D = 15 sec 




wide 




sand 




126 


27, 28 


II 


Jensen 

Filtration 

Plant, Box 

Culvert 

R = 15 km 


4-barrel 
box culvert, 
each 2.6 m 
high, 3.7 m 
wide 




fill 


rein- 
forced 
concrete 


127 


26, 27, 


- 


Jensen 


158 m x 


2-m 


alluvium 


rein- 




28 




Filtration 
Plant, 
Buried 

Reservoir 
R = 15 km 


152 m plan, 
11.4 m high 


cover 




forced 
concrete 



NOTE: 1 mm = 0.04 in.; 1 cm = 0.39 in.; 1 m = 3.28 ft; 1 km = 0.62 mile. 



- 240 ■- 



Surface Shaking Data 


Subsurface Shaking Data 


Surface 


Ground Motion 


Personal 




Underground 


Personal 


Estimated 


Effects 


Parameters 


Perceptions 


Intensity 


Effects 


Perceptions 


Intensity 


(9) 


(10) 


(11) 


(12) 


(13) 


(H) 


(15) 




estimated hori- 




VIII to X 


concrete 








zontal accelera- 




MM I 


spalled and 








tion 0.4g 






longitudinal 
steel ruptured 
or sheared at 
transverse 
construction 
joints 








■I 






spalling at 
top of walls 
due to lateral 
racking 








estimated hori- 




ii 


severe damage 








zontal accelera- 






to roof, col- 








tion 0.4g 






umns, and 
walls, west 
wall pushed in 
about a meter 
at bottom con- 
struction 
joint, many 
columns dam- 
aged at top 
and bottom 







2k] 



Appendix D 

A Short Review of Seismological Terms 

In the real earth, seismic waves emanating from the earthquake source appear 
in a number of forms and travel along a number of paths (see Figure 67). The 
ground motion recorded by a seismograph reflects the passage of waves that have 
traveled along many different paths, all of which compose the motion at the 
location of the recording instrument. The path taken by each wave (or phase) 
depends upon the internal structure of the earth; for example, some waves are 
reflected from the earth's core, and some are reflected from the boundary between 
the earth's crust and underlying mantle. Some wave types owe their existence 
to the fact that the earth has internal structure. If the earth's interior were 
perfectly homogeneous (all properties of the medium independent of position) and 
isotropic (all properties of the medium independent of direction), the surface 
waves recognized by seismologists would not exist at all except for the Rayleigh 
wave. The number of body wave phases recognized on sei smog rams would also be 
greatly reduced in a homogeneous, isotropic earth. One way we can see how 
these various wave types arise is to begin with a very simplified model of the 
earth and see what kinds of waves it can have. Then, by complicating its 
structure by stages, we can see what waves can be added, until we see some of 
the complexity in the real earth. 

We begin with the most uncomplicated earth possible: a homogeneous, isotropic, 
flat earth. We can then build a mathematical model equivalent to this flat 
earth. This model is called a homogeneous, isotropic half-space. It is called 
a half-space because there is a boundary (x„ = 0) below which the homogeneous, 
isotropic medium (in which the waves may propagate) extends to infinity (i.e., 
-°° < x, < °°, -°° < x < °°, < x ? < °°) and above which there is nothing (see 
Figure 67). The surface of the half-space is called a free surface because 
nothing exists above it to place any dynamic constraints upon it; thus it is 
free to move under the influence of waves approaching from below. A full space 
would be one in which the medium exists everywhere. 

It is known that there are two wave types that can exist in an isotropic 
solid: compression (P) and shear (S) waves (proof of this statement would 



- 2^2 - 




*~ oo 



Figure 67- Representation of half-space model and 
associated coordinate system. 



- 243 - 



require a more detailed mathematical treatment appropriate to an introductory 
seismology course and is beyond the intended scope of this appendix). The 
P-waves are characterized by the fact that they excite motion in the particles 
constituting the medium, which is parallel to the direction of propagation of 
the wave. Thus P-waves are actually acoustic or sound waves (see Figure 68). 
S-waves, on the other hand, excite particle motion that is perpendicular, or 
transverse, to their direction of propagation. Because this transverse motion 
can be polarized relative to the path of the wave, S-waves are often identified 
in terms of their vertical (SV) and horizontal (SH) particle motions. Thus, 
there are three types of body waves: P-, SV- , and SH-waves. 

If we now imagine body waves approaching the surface of the half-space from 
below and examine their reflection from the free surface, we find that a 
fourth wave type is possible. This fourth wave type consists of both P and 
SV motion, and its amplitudes decrease exponentially with increasing depth. 
It is a wave that travels parallel to the free surface, and it is called a 
Rayleigh wave. In this stark geometry, it is the only surface wave possible. 
It is the fundamental Rayleigh mode and corresponds to the lowest harmonic at 
which our hypothetical earth's surface may vibrate. A Rayleigh wave consists 
of displacements in a vertical plane, with the horizontal components being 
parallel to the direction of propagation. Shape functions for the components 
are illustrated in Figure 69. The Rayleigh particle motion is basically ellip- 
tic and, in the classical solution for the elastic half-space, is retrograde 
at the surface. The velocity V n of the Rayleigh wave is given approximately 

by 7_ - 0.9 V (for Poisson's ratio approximately equal to 0.25), where V 
n S S 

is the velocity of the shear waves in the same material. 

We may also note in passing that a body wave approaching the free surface from 
below will be reflected, generating a downward- travel ing wave. If the upward- 
traveling wave has some duration, then part of the disturbance will still be 
approaching the free surface, while the reflected part is moving away. The 
actual particle motion in the overlapping region will be the sum of motions con- 
tributed by the incident and reflected parts and will, in general, vary with 
both time and position below the surface. 



- 2kk - 



/ 


//////////////// 


7 


'/////////////// 


/ 


/ 


// 




/ 


































/ 
/ 
































































__ 


V 



a. Undeformed ground 



/ 


/////// / / / ///// 


/ 


//////// / / / ///// 


/ 


/ /////// / / / ///// 




/ 
























/ 














































V 



■S N . /■ V- 



Tension Compression Tension Compression 

Direction of Propagation 

► 

b. Axial deformation due to P-wave 




c. Shear deformation due to S-wave 



Figure 68. Deformation due to body waves 



- 245 - 



Free Surface- 



Particle Motion 
at Surface 



Shape Function for 
Horizontal Motion 




ape Function for 
rtical Motion 



Di rect ion of 



Propagat ion 



Figure 69. Motion due to Rayleigh waves 



- 246 - 



Thus, in the homogeneous, isotropic half-space, the particle motion at some 
point below the free surface could be composed of that due to incident and 
reflected body waves plus that due to passage of the fundamental -mode Rayleigh 
wave. 

Consider now the next order of complication in structure, the layer over a 
half-space (see Figure 70). In this geometry, a large number of possibilities 
exist. The most striking addition is to the family of surface waves. To 
begin with, there are now higher mode Rayleigh waves in addition to the funda- 
mental mode. These higher order modes are analogous to the harmonic overtones 
of a vibrating string. As the order of the mode is increased by one, so are 
the number of nodal depths (depths at which the particle motion is always zero). 
The amplitudes of the particle motions associated with these waves decrease with 
increasing depth. 

In addition to the higher mode Rayleigh waves, with their P-SV particle motion, 
the presence of the layer over half-space geometry now allows the full range 
of surface waves with SH particle motion, beginning with the fundamental mode 
and including all the higher modes. These waves, called Love waves, do not 
exist in the classical elastic half-space as do the Rayleigh waves. Love waves 
arise only when one or more layers of soil or rock of different composition 
exist over the base rock. 

The presence of a layer allows the surface waves to exist in all their modes 
and with the entire range of particle motions (P, SV, SH) . The presence of 
additional layers beyond the first complicates the behavior of the surface 
waves, but only in degree, not in kind. 

If the velocity of seismic waves in the layer is less than in the half-space 
below it, another interesting thing happens. The reflection and refraction of 
seismic waves at a plane interface is controlled by Snell's law: 

sin 0i sin0 2 

— = — - — = constant 

V\ V 2 



- 247 - 



Free Surface 



t 

Layer Thickness 

_J 



x. 



Layer 



Hal f-Space 



x. 



Figure 70. Plane layer over a half-space, 



- 248 - 



where: 

9 , 9 2 = angle of ray paths with vertical, as shown in 
Figure 71 

V , V = wave velocities in medium 1 and medium 2, respec- 
t ively 

If medium 1 is the layer and medium 2 is the half-space, and if V > V , then 
there are values of 8 X for which sin 9 2 > 1,, which is not mathematically permit- 
ted. What does happen is total reflection, which occurs for an angle of inci- 
dence, 9 , larger than the critical angle, 9 . The critical angle is defined by 

(sin e^)" 1 = V ± 



Thus, a body wave that approaches the bottom of the layer with an incident 
angle equal to 9 is refracted along the base of the layer. It will travel 
along the interface of the layer and half-space with speed 7„ but will radiate 
energy back toward the free surface with a reflected angle 9 and a velocity 
V . It is called a head wave and is a common phenomenon. 



There are many other complications introduced by layering, but discussion of 
these is beyond the scope of this appendix. For more details, the interested 
reader is referred to References 4, 114, 196, 197, and 198. 



- 249 - 



Free Surface 




Layer 1 (velocity V ) 



Refracted Wave 



Layer 2 (velocity V ) 



Figure 71. Reflection and refraction of body waves. 



- 250 



Appendix E 

Derivation of the Green's Function for Two-Dimensional SH Motion in a Half-Space 

The Green's function in an infinite elastic medium is given by 

\k 2 R 



G*Ax,t) = ~-2 



fe?6. • 
2 ^J 



R 



\kiR 



•l- _ e "'M 



3x . dx . 
i 3 



R 



(83) 



where: 

p = the mass density of the medium 

uj = the circular frequency 

k\ = w/a = the compression wave number 

kz = w/3 = the shear wave number 

R = VWi - Ci) 2 + (x z - K 2 ) 2 + (« 3 - C 3 ) 2 
= the source to observation point distance 

x = {xi,X2,Xs) = the Cartesian coordinates of the 
observation point 

B, = (B, l ,E, 2 ,E,^) = the Cartesian coordinates of the 
source point 

a = the compression wave velocity 

3 = the shear wave velocity 

Specifically, G Q ..(x,£,) gives the displacement component in the direction i at 
point x due to a "unit" point force acting in the direction j at % for the 
harmonic component of frequency w. The time dependence used herein is e 



First consider constructing the displacement field for a line force acting 
parallel to the 3 direction 



a-:.a,t) - 



f 



Glj{x,t)dZ 3 



(84) 



Introducing the cylindrical, radial distance r in the 1-2 plane, defined as 



r = 



= v 7 ^ - ?1 ) 2 + (x 2 - Qi 



(85) 



- 251 



the integral of Equation (84) can be reduced to the evaluation of 



&: 





/ E ** - r 

«/-00 < 


•iW + (, 3 .e 3 )2 
/ 6 




J_ m y/r 2 + (x 3 - C 3 ) 2 


Then, 


using the substitution 

c i nh t = 





(86) 



(87) 



and recognizing the even and odd behavior of the resulting sine and cosine terms, 
Equation (86) can be expressed as 



«/— 00 



-\k 2 R 



#3 = 2 



JO 



cos [k r cosh {x)]dx 



- 2i 



/ 



sin [k 9 r cosh {x)]di 



(88) 



These two integrals on the right side of Equation (88) are easily recognized as 
integral representations for the Bessel and Neumann functions, 



f° -ikz R r i r n 

/ ^-R-dCa = 2^-Jy (fe 2 r)J - 2i[J«ro(fe 2 r)J 



(89) 



or, alternatively, this can be written in terms of the Hankel function of the 
second kind of order zero as 



-\k 2 R 
W 



dt: 



i-rr#o {kiv) 



(90) 



Using this result to find Equation (84), it should be noted that £ = j = 3. 
Substitution of Equation (90) and its equivalent form for terms involving k\ 
yields 



£3 3 \% > % ) ~ 






(91) 



- 252 - 



Because the second part, involving the derivative with respect to x , is 
independent of x~, it vanishes. This leads to the result 

G*,(*,f) = ^-H { Q 2) (k 2 r) 



33 



*v 



(92) 



where y = p3 2 is the shear modulus of the medium. This result is the Green's 
function for antiplane motion in an infinite medium. 



Now consider finding the Green's function for the semi-infinite medium with a 
traction-free surface at x = 0. The method of images can be effectively used 
for this purpose. Place an image source at £ 3 = -£ 3 (see Figure 72). The 
Green's function for the half-space is thus given by 



"ssK-V*!^ " ^[*0 2 V> + ^ 2 V*> 



(93) 



in which the distance between the image source and observation point is denoted 



by 



r * = >/(*! - ^) 2 + (x 2 + ? 2 ) : 



(9*0 



One check of these results is to verify whether Equation (93) satisfies the 
stress-free boundary condition on xi = 0. For this^ it is required that 



as 



33 



dXr 



= 



x z = 



This derivative is 

3^3 3 



dx 2 **v 

On the free surface x^ - 



H^(fc 2 P)^k. + ^>( fc ^i^ 



(95) 



(96) 



v = 



which is identical to the value for r*. Thus, 



(97) 



- 253 - 



Image Source Point 



Free Surface 




Observation Point 



► 1 



• Source Point 



Figure 72. Image source location, 



- 25^4 - 



9G 



33 



dXr 



Ih. 



Hj 2) (k 2y /( Xl - €l )2 + j|) 



# 2 = 



*i (2) (*2vUi - ^) 2 + c 2 ) 



Hence, this boundary condition is satisfied. 



= 



(98) 



- 255 - 



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Integral Equation Method for Determining Stresses at Tunnel Intersections," 
Proceedings., Second Australian Tunneling Conference, Melbourne, Australia, 
August 1976, pp. 55-64. 

92. Alarcon, E., J. Dominguez, A. Martin, and F. Paris, "Boundary Methods in 
Soil-Structure Interaction, Proceedings, Second International Conference 
on Microzonation, San Francisco, California, November 26 to December 1, 
1978, Vol. 2, pp. 921-932. 

93. Barton, N. , and H. Hansteen, Large Underground Openings at Shallow Depth: 
Comparison of Deformation Magnitudes from Jointed Models and Linear Elastic 
F. E. Analysis, Internal Report No. 54205-5, Norges Geotekniski Institute, 
Oslo, Norway, January 1979. 

94. Daniel, I. M. , "Viscoelastic Wave Interaction wi th Cylindrical Cavity," 
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Engineers, Vol. 92, No. EM6, December 1966, pp. 25-42. 

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95. Okamoto, S., and C. Tamura, "Behavior of Subaqueous Tunnels during Earth- 
quakes," Earthquake Engineering and Structural Dynamics, Vol. 1, 1973. 

96. Okamoto, S., C. Tamura, K. Kato, and M. Hamada, "Behavior of Submerged 
Tunnels During Earthquakes," Proceedings of the Fifth World Conference on 
Earthquake Engineering, Rome, Italy, June 1973. 

97- Wilson, S. D. , F. D. Brown, Jr., and S. D. Schwarz, "In Situ Determination 
of Dynamic Soil Properties," Dynamic Geotechnical Testing, Publication 
STP 654, American Society of Testing and Materials, Philadelphia, Pennsyl- 
vania, 1978, pp. 295-317. 

98. Kanamori, H., and D. L. Anderson, "Importance of Physical Dispersion in 
Surface Wave and Free Oscillation Problems," Reviews of Geophysics and 
Space Physics, Vol. 15, 1977, pp. 105-112. 

99. Seed, H. B. , and I. M. Idriss, Soil Moduli and Damping Factors for Dynamic 
Response Analyses, Report No. EERC 70-10, Earthquake Engineering Research 
Center, University of California, Berkeley, California, 1970. 

100. Silver, M. L. , and T. K. Park, "Testing Procedure Effects on Dynamic Soil 
Behavior," Journal of the Geotechnical Engineering Division, American 
Society of Civil Engineers, Vol. 101, No. GT10, 1975, pp. 1061-1083. 

101. Haimson, B. C. , "Effect of Cyclic Loading on Rock," Dynamic Geotechnical 
Testing, Publication STP 654, American Society of Testing and Materials, 
1978, pp. 228-245. 

102. Drnevich, V. P., B. 0. Hardin, and D. J. Shippy, "Modulus and Damping of 
Soils by Resonant Column Method," Dynamic Geotechnical Testing, Publication 
STP 654, American Society of Testing and Materials, Philadelphia, Pennsyl- 
vania, 1978, pp. 91-125. 

103. Hendron, A. J., Jr., "Mechanical Properties of Rock," Rock Mechanics in 
Engineering Practice, K. G. Stagg and 0. C. Zienkiewicz, eds., John Wiley 
& Sons, New York, New York, 1968, pp. 21-53- 

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10*t. Silver, V. A., S. P. Clemence, and R. W. Stephenson, "Predicting Deforma- 
tions in the Fort Union Formation," Rock Engineering for Foundations and 
Slopes, Vol. 1, American Society of Civil Engineers, New York, New York, 
1968, pp. 13-33. 

105. McDonal, F. J., et al., "Attenuation of Shear and Compressional Waves in 
Pierre Shale," Geophysics, Vol. 23, 1958, pp. 421-^39- 

105. Joyner, W. B., R. E. Warrick, and A. A. Oliver, III, "Analysis of Seismo- 
grams from a Downhole Array in Sediments Near San Francisco Bay," Bulletin 
of the Seismologioal Society of America, Vol. 66, No. 3, June 1976, pp. 937" 
958. 

107. Reiter, L. , and M. E. Monfort, "Variations in Initial Pulse Width as a 
Function of Anelastic Properties and Surface Geology in Central California," 

Bulletin of the Seismologioal Society of America, Vol. 67, 1977, pp. 1319" 
1338. 

108. Stagg, K. G., "In Situ Tests on the Rock Mass," Rock Mechanics in Engineering 
Practice, K. G. Stagg and 0. C. Zienkiewicz, eds., John Wiley & Sons, New 
York, New York, 1968, pp. 125-156. 

109. Brown, E. T., and J. A. Hudson, "Fatigue Failure Characteristics of Some 
Models of Jointed Rock," Earthquake Engineering and Structural dynamics, 
Vol. 2, 1974, pp. 379-386. 

110. Richart, F. E., Jr., D. G. Anderson, and K. H. Stokoe, II, "Predicting 
In Situ St rain- Dependent Shear Moduli of Soil," Proceedings of the Sixth 
World Conference on Earthquake Engineering, New Delhi, India, 1977, 

pp. 2310-2315. 

111. Hardin, B. 0., and V. P. Drnevich, "Shear Modulus and Damping: Measure- 
ment and Parameter Effects," Journal of the Soil Mechanics and Foundations 
Division, American Society of Civil Engineers, Vol. 98, No. SM6, 1972, 

pp. 603-624. 



- 268 - 



112. Miller, R. P., J. H. Troncoso, and R. R. Brown, Jr., "In Situ Impulse Test 
for Dynamic Shear Modulus of Soils," Proceedings of the Conference on In 
Situ Measurement of Soil Properties, Raleigh, North Carolina, Vol. 1, 
American Society of Civil Engineers, New York, New York, 1975, pp. 319-335. 

113- Baecher, G. B., N. A. Lanney, and H. H. Einstein, "Statistical Description 
of Rock Properties and Sampling," Proceedings of the 18th U.S. Symposium 
on Rock Mechanics, Keystone, Colorado, 1977, pp. 5C1-1 to 5C1-8. 

114. Richart, F. E., J. R. Hall, and R. D. Woods, Vibrations of Soils and Foun- 
dations, Prentice-Hall, Englewood Cliffs, New Jersey, 1970, p. 89 (Fig. 3-1 2 *) 

115. Nasu, N. , "Comparative Studies of Earthquake Motions Above-Ground and in 

a Tunnel (Part 1)," Bulletin of the Earthquake Research Institute, Vol. 9, 
Part h, December 1931, pp. ^54-472. 

116. Inouye, W. , "Comparison of Earth Shaking Above Ground and Underground," 
Bulletin of the Earthquake Research Institute, Vol. 12, 193**, pp. 712- 
~]k\ (in Japanese). 

117. Kanai, K. , and T. Tanaka$ "Observations of the Earthquake-Motion at the 
Different Depths of the Earth I ," Bulletin of the Earthquake Research 
Institute, Vol. 29, 1951, pp. 107-113- 

118. Kanai, K., K. Osada, and S. Yoshizawa, "Observations Study of Earthquake 
Motion in the Depth of the Ground IV (Relation between the Amplitude at 
Ground Surface and the Period)," Bulletin of the Earthquake Research Insti- 
tute, Vol. 31, 1953, pp. 228-23^. 

119. Kanai, K. , K. Osada, and S. Yoshizawa, "Observational Study of Earthquake 
Motion in the Depths of the Ground V (The Problem of the Ripple of Earth- 
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1954, pp. 361-370. 



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120. Iwasaki, T., S. Wakabayashi, and F. Tatsuoka, "Characteristics of Under- 
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Effects, H. S. Lew, ed. , U.S. Department of Commerce, Washington, D.C., 
May 1977. 

121. Shima, E. , "Modifications of Seismic Waves in Superficial Soil Layers as 
Verified by Comparative Observations on and Beneath the Surface," Bulletin 
of the Earthquake Research Institute, Vol. *t0, 1962, pp. 187-259- 

122. Kanai, K. , T. Tanaka, S. Yoshizawa, T. Morishita, K. Osada, and T. Suzuki, 
"Comparative Studies of Earthquake Motions on the Ground and Underground II,' 

Bulletin of the Earthquake Research Institute, Vol. hk, 1966, pp. 609-643- 

123- Seed, H. B. , and I. M. Idriss, "Analysis of Ground Motions at Union Bay, 
Seattle, During Earthquakes and Distant Nuclear Blasts," Bulletin of the 
Seismological Society of America, Vol. 60, 1970, pp. 125-136. 

Mh. Tsai, N. C, and G. W. Housner, "Calculation of Surface Motions of a Layered 
Half-Space," Bulletin of the Seismological Society of America, Vol. 60, 
1970, pp. 1625-1651. 

125. Dobry, R., R. V. Whitman, and J. M. Roesset, Soil Properties and the One- 
Dimensional Theory of Earthquake Amplification, Research Report No. R71-18, 
Department of Civil Engineering, Massachusetts Institute of Technology, 
Cambridge, Massachusetts, 1971- 

126. Joyner, W. B., R. E. Warrick, and A. A. Oliver, III, "Analysis of Seismo- 
grams from a Downhole Array in Sediments Near San Francisco Bay," Bulletin 
of the Seismological Society of America, Vol. 66, No. 3, June 1976, pp. 937- 
958. 

127. Blume, J. A., Surface and Subsurface Ground Motion, Engineering Foundation 
Conference on Earthquake Protection of Underground Utility Structure, 
Asilomar, California, September 1972. 



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128. Berardi, R. , F. Capozza, and L. Zonetti , "Analysis of Rock Motion Accelero- 
grams Recorded at Surface and Underground During the 1976 Friuli Seismic 
Period," The 1976 Friuli Earthquake and the Antiseismio Design of Nuclear 
Installations, Rome, Italy, October 1977. 

129. Personal communication from Y. Ichikawa, Electric Power Development Company, 
Ltd., Tokyo, Japan, to G.^N. Owen, URS/John A. Blume & Associates, Engi- 
neers, San Francisco, California, Job File No. 7821, October 1979- 

130. Personal communication from T. Iwasaki, Public Works Research Institute, 
Tsukuba, Japan, to G. N. Owen, URS/John A. Blume & Associates, Engineers, 
San Francisco, California, Job File No. 7821, June 1978. 

131. Nakano K. , and Y. Kitagawa, "Earthquake Observation System In and Around 
Structures in Japan," presented at the 11th Joint Meeting, U.S. -Japan 
Panel on Wind and Seismic Effects, Tokyo, Japan, September k-~l , 1979- 

132. O'Brien, L. J., and J. Saunier, "Comparison of Predicted and Observed 
Subsurface-Surface Seismic Spectral Ratios," NV0-624-2, prepared for 
Nevada Operations Office, U.S. Department of Energy, Las Vegas, Nevada, 
March 1980. 

133- Gilbert, F. , and L. Knopoff, "Scattering of Impulsive Elastic Waves by a 
Rigid Cylinder," Journal of the Acoustical Society of America, Vol. 31, 
No. 9, September 1959, pp. 1169-1175- 

134. Gilbert, F. , "Scattering of Impulsive Elastic Waves by a Smooth Convex 
Cylinder," Journal of the Acoustical Society of America, Vol. 32, No. 7, 
July 1960, pp. 841-857. 

135- Banaugh, R. P., and W. Goldsmith, "Diffraction of Steady Acoustic Waves 
by Surfaces of Arbitrary Shape," Journal of the Acoustical Society of 
America, Vol. 35, No. 10, October 1963, pp. 1590-1601. 



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136. Garnet, H. , and J. Crouzet-Pascal , "Transient Response of a Circular 
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tional Wave," Journal of Applied Mechanics, American Society of Mechanical 
Engineers, Vol. 33, September 1966, pp. 521-531. 

137. Niwa, Y. , S. Kobayashi , and T. Fukui, "Applications of Integral Equation 
Method to Some Geomechanical Problems," Numerical Methods in Geomechanics , 
C. S. Desai, ed. , Vol. 1, American Society of Civil Engineers, New York, 
New York, 1976, pp. 120-131. 

138. Yoshihara, T. , A. R. Robinson, and J. L. Merritt, Interaction of Plane 
Elastic Waves with an Elastic Cylindrical Shell, Technical Report No. 
SRS 261, Department of Civil Engineering, University of Illinois, Cham- 
paign, Illinois, January 1963- 

139. American Association of State Highway and Transportation Officials, Stan- 
dard Specifications for Highway Bridges, 11th edition, Washington, D.C., 
1973. 

1A0. Department of General Services, State of California Administrative Code, 

Title 2k (Building Standards), Office of Administrative Hearing, Sacramento, 
California, 1979- 

1^1. Structural Engineers Association of California, Recommended Lateral Force 
Requirements and Commentary, San Francisco, California, 1976. 

142. Japan Society of Civil Engineers, Specifications for Earthquake Resistant 
Design of Submerged Tunnels, Tokyo, Japan, March 1975- 

1 43 - Japan Society of Civil Engineers, Earthquake Resistant Design Features of 
Submerged Tunnels in Japan, Tokyo, Japan, 1977. 

\hh. Personal communication from G. J. Murphy, Parsons, Brinckerhoff , Quade & 
Douglas, San Francisco, California, to G. N. Owen, URS/John A. Blume S 
Associates, Engineers, San Francisco, California, Job File No. 7821, 
January 1980. 

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1^5. Kuribayashi, E., and K. Kawashima, Earthquake Resistant Design of Submerged 
Tunnels and an Example of Its Application, PWRI Technical Memorandum No. 
1169, Public Works Research Institute, Tsukuba, Japan, November 1976. 

1 46. Kuribayashi, E. , T. Iwasaki , and K. Kawashima, "Earthquake Resistance of 
Subsurface Tubular Structure," Proceedings of the Sixth World Conference 
on Earthquake Engineering, New Delhi, India, January 1 977 - 

1^7. Kuribayashi, E., K. Kawashima, and Shibata, Sectional Forces in a Submerged 
Tunnel by the Seismic Deformation Method, PWRI Technical Memorandum No. 
1193, Public Works Research Institute, Tsukuba, Japan, March 1977 (in 
Japanese) . 

148. Kuribayashi, E. , K. Kawashima, Shibata, and Miyata, A Study of Ultimate 
Strength of a Submerged Tunnel Using the Seismic Deformation Method, PWRI 
Technical Memorandum No. 1253, Public Works Research Institute, Tsukuba, 
Japan, April 1977 (in Japanese). 

149. Kuribayashi, E. , K. Kawashima, and Shibata, The Influence of a Flexible 
Connection on the Sectional Forces in a Submerged Tunnel, PWRI Technical 
Memorandum No. 1272, Public Works Research Institute, Tsukuba, Japan, 
February 1978 (in Japanese). 

150. Seed, H. B., and R. V. Whitman, "Design of Earth Retaining Structures for 
Dynamic Loads," Lateral Stresses in the Ground and Design of Earth-Retaining 
Structures, American Society of Civil Engineers, New York, New York, 1970. 

151. Aoki, Y. , and S. Hayashi, "Spectra for Earthquake-Resistive Design of Under- 
ground Long Structures," Proceedings of the Fifth World Conference on Earth- 
quake Engineering, Rome, Italy, June 1 973 - 

152. Hamada, M. , T. Akimoto, and H. Izumi, "Dynamic Stress of a Submerged Tunnel 
During Earthquakes," Proceedings of the Fifth World Conference on Earthquake 
Engineering, Rome, Italy, June 1973. 



273 - 



153- Goto, Y. , J. Ota, and T. Sato, "On Earthquake Response of Submerged 

Tunnels," Proceedings of the Fifth World Conference on Earthquake Engi- 
neering, Rome, Italy, June 1973. 

154. Douglas, W. S., and R. Warshaw, "Design of Seismic Joint for San Francisco 
Bay Tunnel," Journal of the Structural Division, American Society of Civil 
Engineers, Vol. 97, No. ST4, April 1971, pp. 1129-1141 (p. 1131, Fig. 2). 

155. Roark, R. J., and W. C. Young, Formulas for Stress and Strain, 5th edition, 
McGraw-Hill, New York, New York, 1975. 

156. East Bay Municipal Utility District, Seismic Design Requirements, Oakland, 
California, May 1 973 - 

157. Personal communication from J. M. Keith, Vice President, URS/John A. Blume & 
Associates, Engineers, San Francisco, California, to G. N. Owen, URS/John A. 
Blume & Associates, Engineers, San Francisco, California, Job File No. 7821, 
January 198O. 

158. Dames & Moore, Interpretive Report — Engineering Recommendations , NSOC-N-2, 
Los Angeles, California, prepared for the San Francisco Wastewater Program, 
Department of Public Works, San Francisco, California, March 1979. 

159. Personal communication from F. Moss, Department of Public Works, San Fran- 
cisco, California, to G. N. Owen, URS/John A. Blume & Associates, Engineers, 
San Francisco, California, Job File No. 7821, December 28, 1979. 

160. Personal communication from D. J. Birrer, Department of Public Works, San 
Francisco, California, to G. N. Owen, URS/John A. Blume & Associates, Engi- 
neers, San Francisco, California, Job File No. 7821, January 17, 1980. 

161. Dames & Moore, Supplementary Soils Report, NSOC-N-4 (Marina Boulevard), 

Los Angeles, California, prepared for the San Francisco Wastewater Program, 
Department of Public Works, San Francisco, California, November 1979- 



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1 62. Ranken, R. E., and J. Ghaboussi, Tunnel Design Considerations: Analysis 
of Stresses and Deformations Around Advancing Tunnels, FRS-OR&D 75-84, 
Federal Railroad Administration, U.S. Department of Transportation, 
Washington, D.C., August 1975. 

163. Ranken, R. E., J. Ghaboussi, and A. J. Hendron, Jr., Analysis of Ground- 
Liner Interaction for Tunnels, UMTA- I L-06-0043-78-3, Urban Mass Transporta- 
tion Administration, U.S. Department of Transportation, Washington, D.C., 
October 1978. 

164. Einstein, H. H., and C. W. Schwartz, "Simplified Analysis for Tunnel Sup- 
ports," Journal of the Geoteohnieal Engineering Division, American Society 
of Civil Engineers, Vol. 105, No. GT4, April 1979, pp. 499"518. 

165. Schwartz, C. W., and H. H. Einstein, Simplified Analysis for Ground- 
Structure Interaction in Tunneling, R79-27, Department of Civil Engineer- 
ing, Massachusetts Institute of Technology, Cambridge, Massachusetts, 
June 1979. 

166. Schwartz, C. W. , A. S. Azzouz, and H. H. Einstein, Aspects of Yielding in 
Ground- Structure Interaction, R79 - 28, Department of Civil Engineering, 
Massachusetts Institute of Technology, Cambridge, Massachusetts, June 1979. 

167. Einstein, H. H., W. Steiner, and G. B. Baecher, "Assessment of Empirical 
Design Methods for Tunnels in Rock," Proceedings of the 1979 Rapid Excava- 
tion and Tunneling Conference, Atlanta, Georgia, Vol. 1, American Institute 
of Mining, Metallurgical, and Petroleum Engineers, Inc., New York, New York, 
1979, PP. 683-706. 

168. Owen, G. N., R. E. Schol 1 , and T. L. Brekke, "Earthquake Engineering of 
Tunnels," Proceedings of the 1979 Rapid Excavation and Tunneling donference, 
Atlanta, Georgia, Vol. 1, American Institute of Mining, Metallurgical, and 
Petroleum Engineers, Inc., New York, New York, 1979, PP« 709-721 (pp. 714- 

715, Figs. 4, 5). 



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169. Vick, S. G., A Probabilistic Approach to Geology in Hard-Rock Tunneling, 
R75-11, Department of Civil Engineering, Massachusetts Institute of 
Technology, Cambridge, Massachusetts, June 1 974. 

170. Dendrou, B. , Integrated Approach to Cavity System Seismic Evaluation, 
FHWA-RD-78-159, Federal Highway Administration, U.S. Department of Trans- 
portation, Washington, D.C., October 1978. 

1 71 - Jansen, R. B., "Earthquake Protection of Water and Sewage Lifelines," 

The Current State of Knowledge of Lifeline Earthquake Engineering. Ameri- 
can Society of Civil Engineers, New York, New York, 1977, pp. 136-149. 

172. Department of Water Resources, California State Water Project, Vol. 2, 
Bulletin No. 200, Sacramento, California, November 1974. 

173. Department of Water Resources, California Aqueduct, Tehachapi Division, 
Beartrap Access Structure, Drawing No. Q-12P1-1, Sacramento, California, 
Revised March 24, 1972. 

174. Kuesel, T. R., "Structural Design of the Bay Area Rapid Transit System," 
Civil Engineering, American Society of Civil Engineers, New York, New York, 
April 1968, pp. 46-50. 

175. Anton, W. F., "A Utility's Preparation for a Major Earthquake," Journal of 
the American Water Works Association, June 1978, pp. 311-314. 

176. Personal communication from W. F. Anton, Director of Engineering, East 
Bay Municipal Utility District, Oakland, California, to G. N. Owen, URS/ 
John A. Blume & Associates, Engineers, San Francisco, California, Job 
File No. 7821, December 1979- 

177. Hradilek, P. J., "Behavior of Underground Box Conduit in the San Fernando 
Earthquake," The Current State of Knowledge of Lifeline Earthquake Engi- 
neering, American Society of Civil Engineers, New York, New York, 1977, 
pp. 308-319. 



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178. Terzaghi, K. , and F. E. Richart, Jr., "Stresses in Rock About Cavities," 
Geotechnique , Vol. 3, 1952, pp. 57*90. 

179. Terzaghi, K. , "Rock Defects and Loads on Tunnel Supports," Rock Tunneling 
with Steel Supports, R. V. Proctor and T. L. White, eds., Commercial 
Sheaving and Stamping Company, Youngstown, Ohio, 19^6, revised 1 968 . 

180. Rabcewicz, L. V., "Principals of Dimensioning the Support System for the 
New Austrian Tunneling Method," Water Power, Vol. 25, No. 3, March 1973, 
pp. 88-93. 

181. Barton, N. R., R. Lien, and J. Lunde, Engineering Classification of Rock 
Masses for the Design of Tunnel Support, Report No. 106, Norwegian Geo- 
technical Institute, Oslo, Norway, 1974. 

182. Bieniawski, Z. T., "Rock Mass Classifications in Rock Engineering," 

Proceedings of the Symposium on Exploration for Rock Engineering , 
Johannesburg, South Africa, November 1976, pp. 97-106. 

183. Wickham, G. E., H. R. Tiedemann, and E. H. Skinner, "Ground Support 
Prediction Model — RSR Concept," Proceedings of the 1974 Rapid Excavation 
and Tunneling Conference, American Institute of Mining, Metallurgical, 
and Petroleum Engineers, Inc., New York, New York, 1974, pp. 691-707. 

1 84. Wittke, W. , "Static Analysis for Underground Openings in Jointed Rock," 
Numerical Methods in Geotechnical Engineering, C. S. Desai and J. T. 
Christian, eds., McGraw-Hill, New York, New York, 1977, pp. 589-638. 

185. Wittke, W. , and B. Pierau, "3-D Stability Analysis of Tunnels in Jointed 
Rock," Numerical Methods in Geomechanics , C. S. Desai, ed. , Vol. 3, Ameri- 
can Society of Civil Engineers, New York, New York, 1976, pp. 1 401 - 1 41 8 . 

186. Proctor, R. V., and T. L. White, Earth Tunneling with Steel Supports, 
Commercial Sheaving, Inc., Youngstown, Ohio, 1977. 



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1 87 - Terzaghi, K. , Theoretical Soil Mechanics, John Wiley & Sons, New York, 
New York, 19^3 (ninth printing, 1959). 

188. Brekke, T. L. , and G. E. Korbin, Seismic Instrumentation of Transportation 
Tunnels in California, Berkeley, California, prepared for the Federal High- 
way Administration, Office of Research, Structures and Applied Mechanics 
Division, Washington, D.C., August 1977. 

189. Thomson, W. T., "Transmission of Elastic Waves Through a Stratified Solid 
Medium," Journal of Applied Physics, Vol. 21, 1950, pp. 89-93. 

190. Haskell, N. A., "The Dispersion of Surface Waves on Multi layered Media," 

Bulletin of the Seismological Society of America, Vol. **3, 1953, pp. 17 - ^. 

191. Chang Tsai-yung and Chen Da-sheng, General Features of the Tangshan 
Earthquake, Academia Sinica, Institute of Engineering Mechanics, Harbin, 
China, July 1978. 

192. Steinhardt, 0. W. , and N. F. Sweeney, "Effects of October k, 1978, Earth- 
quake on Helms Pumped Storage Power Plant Site," Earthquake Engineering 
Research Institute Newsletter, Vol. 13, No. 1, January 1979. 

193. Personal communication from P. I. Yanev, URS/John A. Blume & Associates, 
Engineers, San Francisco, California, to G. N. Owen, URS/John A. Blume & 
Associates, Engineers, San Francisco, California, Job File No. 7821, 
October 1979. 

194. Ambraseys, N. N., "The Gemono-Fr iul i (Italy) Earthquake of 6 May 1976," 
Proceedings, CENTO Seminar on Recent Advances on Earthquake Hazard 
Minimization, Tehran, Iran, November 1976. 

195. Personal communication from L. Mazzini, Marin Historical Society, 

San Rafael, California, to G. N. Owen, URS/John A. Bljjme & Associates, 
Engineers, San Francisco, California, Job File No. 7821, April 25, 1979- 



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196. Ewing, W. M., W. S. Jardetzky, and F. Press, Elastic Waves in Layered 
Media, McGraw-Hill, New York, New York, 1957. 

197. Fung, Y. C, Foundations of Solid Mechanics , Prentice-Hall, Englewood 
Cliffs, New Jersey, 1 965 . 

198. Kolsky, H., Stress Waves in Solids, Dover Publications, New York, New 
York, 1963. 



279 



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FEDERALLY COORDINATED PROGRAM (FCP) OF HIGHWAY 
RESEARCH AND DEVELOPMENT 



The Offices of Research and Development (R&D) of 
the Federal Highway Administration (FHWA) are 
responsible for a broad program of staff and contract 
research and development and a Federal-aid 
program, conducted by or through the State highway 
transportation agencies, that includes the Highway 
Planning and Research (HP&R) program and the 
National Cooperative Highway Research Program 
(NCHRP) managed by the Transportation Research 
Hoard. The FCP is a carefully selected group of proj- 
ects that uses research and development resources to 
obtain timely solutions to urgent national highway 
engineering problems.* 

The diagonal double stripe on the cover of this report 
represents a highway and is color-coded to identify 
the FCP category that the report falls under. A red 
stripe is used for category 1, dark blue for category 2, 
light blue for category 3, brown for category 4, gray 
for category 5, green for categories 6 and 7, and an 
orange stripe identifies category 0. 

FCP Category Descriptions 

1. Improved Highway Design and Operation 
for Safety 

Safety R&D addresses problems associated with 
the responsibilities of the FHWA under the 
Highway Safety Act and includes investigation of 
appropriate design standards, roadside hardware, 
signing, and physical and scientific data for the 
formulation of improved safety regulations. 

2. Reduction of Traffic Congestion, and 
Improved Operational Efficiency 

Traffic R&D is concerned with increasing the 
operational efficiency of existing highways by 
advancing technology, by improving designs for 
existing as well as new facilities, and by balancing 
the demand-capacity relationship through traffic 
management techniques such as bus and carpool 
preferential treatment, motorist information, and 
rerouting of traffic. 

3. Environmental Considerations in Highway 
Design, Location, Construction, and Opera- 
tion 

Environmental R&D is directed toward identify- 
ing and evaluating highway elements that affect 



* The complete seven-volume official statement of the FCP is available from 
the National Technical Information Service, Springfield, Va. 22161. Single 
copies of the introductory volume are available without charge from Program 
Analysis (HRD-3), Offices of Research and Development, Federal Highway 
Administration, Washington, D.C. 20590. 



the quality of the human environment. The goals 
are reduction of adverse highway and traffic 
impacts, and protection and enhancement of the 
environment. 

4. Improved Materials Utilization and 
Durability 

Materials R&D is concerned with expanding the 
knowledge and technology of materials properties, 
using available natural materials, improving struc- 
tural foundation materials, recycling highway 
materials, converting industrial wastes into useful 
highway products, developing extender or 
substitute materials for those in short supply, and 
developing more rapid and reliable testing 
procedures. The goals are lower highway con- 
struction costs and extended maintenance-free 
operation. 

5. Improved Design to Reduce Costs, Extend 
Life Expectancy, and Insure Structural 
Safety 

Structural R&D is concerned with furthering the 
latest technological advances in structural and 
hydraulic designs, fabrication processes, and 
construction techniques to provide safe, efficient 
highways at reasonable costs. 

6. Improved Technology for Highway 
Construction 

This category is concerned with the research, 
development, and implementation of highway 
construction technology to increase productivity, 
reduce energy consumption, conserve dwindling 
resources, and reduce costs while improving the 
quality and methods of construction. 

7. Improved Technology for Highway 
Maintenance 

This category addresses problems in preserving 
the Nation's highways and includes activities in 
physical maintenance, traffic services, manage- 
ment, and equipment. The goal is to maximize 
operational efficiency and safety to the traveling 
public while conserving resources. 

0. Other New Studies 

This category, not included in the seven-volume 
official statement of the FCP, is concerned with 
HP&R and NCHRP studies not specifically related 
to FCP projects. These studies involve R&D 
support of other FHWA program office research. 



DOT LIBRARY 



00Q570QA